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Dissertations / Theses on the topic 'Linear algebraic groups'
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1
Turner, S. M. "Hasse-Weil zeta functions for linear algebraic groups." Thesis, University of Glasgow, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.318888.
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Haller, Sergei. "Computing Galois cohomology and forms of linear algebraic groups." Giessen Giessener Elektronische Bibliothek, 2005. http://geb.uni-giessen.de/geb/volltexte/2005/2474/index.html.
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Gandhi, Raj. "Oriented Cohomology Rings of the Semisimple Linear Algebraic Groups of Ranks 1 and 2." Thesis, Université d'Ottawa / University of Ottawa, 2021. http://hdl.handle.net/10393/42566.
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In this thesis, we compute minimal presentations in terms of generators and relations for the oriented cohomology rings of several semisimple linear algebraic groups of ranks 1 and 2 over algebraically closed fields of characteristic 0. The main tools we use in this thesis are the combinatorics of Coxeter groups and formal group laws, and recent results of Calm\`es, Gille, Petrov, Zainoulline, and Zhong, which relate the oriented cohomology rings of flag varieties and semisimple linear algebraic groups to the dual of the formal affine Demazure algebra.
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Henes, Matthew Thomas. "Root subgroups of the rank two unitary groups." CSUSB ScholarWorks, 2005. https://scholarworks.lib.csusb.edu/etd-project/2841.
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Discusses certain one-parameter subgroups of the low-rank unitary groups called root subgroups. Unitary groups also have representations of Lie type which means they consist of transformations that act as automorphisms of an underlying Lie algebra, in this case the special linear algebra. Exploring this definition of the unitary groups, we find a correlation, via exponentiation, to the basis elements of Lie algebra.
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Junkins, Caroline. "The Grothendieck Gamma Filtration, the Tits Algebras, and the J-invariant of a Linear Algebraic Group." Thesis, Université d'Ottawa / University of Ottawa, 2014. http://hdl.handle.net/10393/31331.
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Consider a semisimple linear algebraic group G over an arbitrary field F, and a projective homogeneous G-variety X. The geometry of such varieties has been a consistently active subject of research in algebraic geometry for decades, with significant contributions made by Grothendieck, Demazure, Tits, Panin, and Merkurjev, among others. An effective tool for the classification of these varieties is the notion of a cohomological (or alternatively, a motivic) invariant. Two such invariants are the set of Tits algebras of G defined by J. Tits, and the J-invariant of G defined by Petrov, Semenov, and Zainoulline. Quéguiner-Mathieu, Semenov and Zainoulline discovered a connection between these invariants, which they developed through use of the second Chern class map.
The first goal of the present thesis is to extend this connection through the use of higher Chern class maps. Our main technical tool is the Steinberg basis, which provides explicit generators for the γ-filtration on the Grothendieck group K_0(X) in terms of characteristic classes of line bundles over X. As an application, we establish a connection between the J-invariant and the Tits algebras of a group G of inner type E6.
The second goal of this thesis is to relate the indices of the Tits algebras of G to nontrivial torsion elements in the γ-filtration on K_0(X). While the Steinberg basis provides an explicit set of generators of the γ-filtration, the relations are not easily computed. A tool introduced by Zainoulline called the twisted γ-filtration acts as a surjective image of the γ-filtration, with explicit sets of both generators and relations. We use this tool to construct torsion elements in the degree 2 component of the γ-filtration for groups of inner type D2n. Such a group corresponds to an algebra A endowed with an orthogonal involution having trivial discriminant. In the trialitarian case (i.e. type D4), we construct a specific element in the γ-filtration which detects splitting of the associated Tits algebras. We then relate the non-triviality of this element to other properties of the trialitarian triple such as decomposability and hyperbolicity.
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Opalecky, Robert Vincent. "A Topological Uniqueness Result for the Special Linear Groups." Thesis, University of North Texas, 1997. https://digital.library.unt.edu/ark:/67531/metadc278561/.
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The goal of this paper is to establish the dependency of the topology of a simple Lie group, specifically any of the special linear groups, on its underlying group structure. The intimate relationship between a Lie group's topology and its algebraic structure dictates some necessary topological properties, such as second countability. However, the extent to which a Lie group's topology is an "algebraic phenomenon" is, to date, still not known.
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Wagner, David R. "Schur Rings Over Projective Special Linear Groups." BYU ScholarsArchive, 2016. https://scholarsarchive.byu.edu/etd/6089.
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This thesis presents an introduction to Schur rings (S-rings) and their various properties. Special attention is given to S-rings that are commutative. A number of original results are proved, including a complete classification of the central S-rings over the simple groups PSL(2,q), where q is any prime power. A discussion is made of the counting of symmetric S-rings over cyclic groups of prime power order. An appendix is included that gives all S-rings over the symmetric group over 4 elements with basic structural properties, along with code that can be used, for groups of comparatively small order, to enumerate all S-rings and compute character tables for those S-rings that are commutative. The appendix also includes code optimized for the enumeration of S-rings over cyclic groups.
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Illengo, Marco. "Diophantine Analysis and Linear Groups." Doctoral thesis, Scuola Normale Superiore, 2008. http://hdl.handle.net/11384/85693.
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Housley, Matthew L. "Conjugacy Classes of the Piecewise Linear Group." Diss., CLICK HERE for online access, 2006. http://contentdm.lib.byu.edu/ETD/image/etd1442.pdf.
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Massold, Heinrich. "Labile und relative Reduktionstheorie über Zahlkörpern." Bonn : Mathematisches Institut der Universität, 2003. http://catalog.hathitrust.org/api/volumes/oclc/54890700.html.
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Kundu, Subiman. "Spaces of continuous linear functionals on function spaces." Diss., Virginia Polytechnic Institute and State University, 1989. http://hdl.handle.net/10919/54225.
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This thesis is a study of several spaces of continuous linear functionals on various function spaces with a natural norm inherited from a larger Banach space. The completeness of these normed linear spaces is studied in detail and several necessary and sufficient conditions are obtained in this regard. Since spaces of continuous linear functionals are inherently related to spaces of measures, their measure-theoretic counterparts are also studied. By using these counterparts, several necessary and sufficient conditions are obtained on the separability of these spaces of continuous linear functionals.Ph. D.
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Kley, Marius [Verfasser], and Peter [Akademischer Betreuer] Schneider. "Etale (Phi, Gamma)-modules with values in linear algebraic groups / Marius Kley ; Betreuer: Peter Schneider." Münster : Universitäts- und Landesbibliothek Münster, 2019. http://d-nb.info/1202075320/34.
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De, Saedeleer Julie. "The residually weakly primitive and locally two-transitive rank two geometries for the groups PSL(2, q)." Doctoral thesis, Universite Libre de Bruxelles, 2010. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210037.
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The main goal of this thesis is a contribution to the classification of all incidence geometriesof rank two on which some group PSL(2,q), q a prime power, acts flag-transitively.
Actually we require that the action be RWPRI (residually weakly primitive) and (2T)1
(doubly transitive on every residue of rank one). In fact our definition of RWPRI requires
the geometry to be firm (each residue of rank one has at least two elements) and RC
(residually connected).
The main goal is achieved in this thesis.
It is stated in our "Main Theorem". The proof of this theorem requires more than 60pages.
Quite surprisingly, our proof in the direction of the main goal uses essentially the classification
of all subgroups of PSL(2,q), a famous result provided in Dickson’s book "Linear groups: With an exposition of the Galois field theory", section 260, in which the group is called Linear Fractional Group LF(n, pn).
Our proof requires to work with all ordered pairs of subgroups up to conjugacy.
The restrictions such as RWPRI and (2T)1 allow for a complete analysis.
The geometries obtained in our "Main Theorem" are bipartite graphs; and also locally 2-arc-transitive
graphs in the sense of Giudici, Li and Cheryl Praeger. These graphs are interesting in their own right because of
the numerous connections they have with other fields of mathematics.
Doctorat en Sciences
info:eu-repo/semantics/nonPublished
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Loisel, Benoit. "Sur les sous-groupes profinis des groupes algébriques linéaires." Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLX024/document.
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Dans cette thèse, nous nous intéressons aux sous-groupes profinis et pro-p d'un groupe algébrique linéaire connexe défini sur un corps local. Dans le premier chapitre, on résume brièvement la théorie de Bruhat-Tits et on introduit les notations nécessaires à ce travail. Dans le second chapitre, on trouve des conditions équivalentes à l'existence de sous-groupes compacts maximaux d'un groupe algébrique linéaire G connexe quelconque défini sur un corps local K. Dans le troisième chapitre, on obtient un théorème de conjugaison des sous-groupes pro-p maximaux de G(K) lorsque G est réductif. On décrit ces sous-groupes, de plus en plus précisément, en supposant successivement que G est semi-simple, puis simplement connexe, puis quasi-déployé. Dans le quatrième chapitre, on s'intéresse aux présentations d'un sous-groupe pro-p maximal du groupe des points rationnels d'un groupe algébrique G semi-simple simplement connexe quasi-déployé défini sur un corps local K. Plus spécifiquement, on calcule le nombre minimal de générateurs topologiques d'un sous-groupe pro-p maximal. On obtient une formule linéaire en le rang d'un certain système de racines, qui dépend de la ramification de l'extension minimale L=K déployant G, explicitant ainsi les contributions de la théorie de Lie et de l'arithmétique du corps de baseIn this thesis, we are interested in the profinite and pro-p subgroups of a connected linear algebraic group defined over a local field. In the first chapter, we briefly summarize the Bruhat-Tits theory and introduce the notations necessary for this work. In the second chapter we find conditions equivalent to the existence of maximal compact subgroups of any connected linear algebraic group G defined over a local field K. In the third chapter, we obtain a conjugacy theorem of the maximal pro-p subgroups of G(K) when G is reductive. We describe these subgroups, more and more precisely, assuming successively that G is semi-simple, then simply connected, then quasi-split in addition. In the fourth chapter, we are interested in the pro-p presentations of a maximal pro-p subgroup of the group of rational points of a quasi-split semi-simple algebraic group G defined over a local field K. More specifically, we compute the minimum number of generators of a maximal pro-p subgroup. We obtain a formula which is linear in the rank of a certain root system, which depends on the ramification of the minimal extension L=K which splits G, thus making explicit the contributions of the Lie theory and of the arithmetic of the base field
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Lourdeaux, Alexandre. "Sur les invariants cohomologiques des groupes algébriques linéaires." Thesis, Lyon, 2020. http://www.theses.fr/2020LYSE1044.
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Notre thèse s'intéresse aux invariants cohomologiques des groupes algébriques linéaires, lisses et connexes sur un corps quelconque. Plus spécifiquement on étudie les invariants de degré 2 à coefficients dans le complexe de faisceaux galoisiens Q/Z(1), c'est-à-dire des invariants à valeurs dans le groupe de Brauer. Pour se faire on utilise la cohomologie étale des faisceaux sur les schéma simpliciaux. On obtient une description de ces invariants pour tous les groupes linéaires, lisses et connexes, notamment les groupes non réductifs sur un corps imparfait (par exemple les groupes pseudo-réductifs ou unipotents).On se sert de la description établie pour étudier le comportement du groupe des invariants à valeurs dans le groupe de Brauer par des opérations sur les groupes algébriques. On explicite aussi ce groupe d'invariants pour certains groupes algébriques non réductifs sur un corps imparfaitOur thesis deals with the cohomological invariants of smooth and connected linear algebraic groups over an arbitrary field. More precisely, we study degree 2 invariants with coefficients Q/Z(1), that is invariants taking values in the Brauer group. Our main tool is the étale cohomology of sheaves on simplicial schemes. We get a description of these invariants for every smooth and connected linear groups, in particular for non reductive groups over an imperfect field (as pseudo-reductive or unipotent groups for instance).We use our description to investigate how the groups of invariants with values in the Brauer group behave with respect to operations on algebraic groups. We detail this group of invariants for particular non reductive algebraic groups over an imperfect field
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Brown, Scott. "Finite reducible matrix algebras." University of Western Australia. School of Mathematics and Statistics, 2006. http://theses.library.uwa.edu.au/adt-WU2006.0079.
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[Truncated abstract] A matrix is said to be cyclic if its characteristic polynomial is equal to its minimal polynomial. Cyclic matrices play an important role in some algorithms for matrix group computation, such as the Cyclic Meataxe of Neumann and Praeger. In 1999, Wall and Fulman independently proved that the proportion of cyclic matrices in general linear groups over a finite field of fixed order q has limit [formula] as the dimension approaches infinity. First we study cyclic matrices in maximal reducible matrix groups, that is, the stabilisers in general linear groups of proper nontrivial subspaces. We modify Wall’s generating function approach to determine the limiting proportion of cyclic matrices in maximal reducible matrix groups, as the dimension of the underlying vector space increases while that of the invariant subspace remains fixed. This proportion is found to be [formula] note the change of the exponent of q in the leading term of the expansion. Moreover, we exhibit in each maximal reducible matrix group a family of noncyclic matrices whose proportion is [formula]. Maximal completely reducible matrix groups are the stabilisers in a general linear group of a nontrivial decomposition U1⊕U2 of the underlying vector space. We take a similar approach to determine the limiting proportion of cyclic matrices in maximal completely reducible matrix groups, as the dimension of the underlying vector space increases while the dimension of U1 remains fixed. This limiting proportion is [formula]. ... We prove that this proportion is[formula] provided the dimension of the fixed subspace is at least two and the size q of the field is at least three. This is also the limiting proportion as the dimension increases for separable matrices in maximal completely reducible matrix groups. We focus on algorithmic applications towards the end of the thesis. We develop modifications of the Cyclic Irreducibility Test - a Las Vegas algorithm designed to find the invariant subspace for a given maximal reducible matrix algebra, and a Monte Carlo algorithm which is given an arbitrary matrix algebra as input and returns an invariant subspace if one exists, a statement saying the algebra is irreducible, or a statement saying that the algebra is neither irreducible nor maximal reducible. The last response has an upper bound on the probability of incorrectness.
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Ramirez, Jessica Luna. "CONSTRUCTIONS AND ISOMORPHISM TYPES OF IMAGES." CSUSB ScholarWorks, 2015. https://scholarworks.lib.csusb.edu/etd/254.
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In this thesis, we have presented our discovery of true finite homomorphic images of various permutation and monomial progenitors, such as 2*7: D14, 2*7 : (7 : 2), 2*6 : S3 x 2, 2*8: S4, 2*72: (32:(2S4)), and 11*2 :m D10. We have given delightful symmetric presentations and very nice permutation representations of these images which include, the Mathieu groups M11, M12, the 4-fold cover of the Mathieu group M22, 2 x L2(8), and L2(13). Moreover, we have given constructions, by using the technique of double coset enumeration, for some of the images, including M11 and M12. We have given proofs, either by hand or computer-based, of the isomorphism type of each image. In addition, we use Iwasawa's Lemma to prove that L2(13) over A5, L2(8) over D14, L2(13) over D14, L2(27) over 2D14, and M11 over 2S4 are simple groups. All of the work presented in this thesis is original to the best of our knowledge.
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Kurujyibwami, Célestin. "Group classification of linear Schrödinger equations by the algebraic method." Licentiate thesis, Linköpings universitet, Matematiska institutionen, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-125136.
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This thesis is devoted to the group classification of linear Schrödinger equations. The study of Lie symmetries of such equations was initiated more than 40 years ago using the classical Lie infinitesimal method for specific types of real-valued potentials. In first papers on this subject, most attention was paid to dynamical transformations, which necessarily change the time and space variables. This is why phase translations were missed. Later, the study of Lie symmetries was extended to nonlinear Schrödinger equations. At the same time, the group classification problem for the class of linear Schrödinger equations with complex potentials remains unsolved. The aim of the present thesis is to carry out the group classification for the class of linear Schrödinger equations with complex potentials. These potentials are nowadays important in quantum mechanics, scattering theory, condensed matter physics, quantum field theory, optics, electromagnetics and so forth. We exhaustively solve the group classification problem for space dimensions one and two. The thesis comprises two parts. The first part is a brief review of Lie symmetries and group classification of differential equations. Next, we outline the equivalence transformations in a class of differential equations, normalization properties of such class and the algebraic method for group classification of differential equations. The second part consists of two research papers. In the first paper, the algebraic method is applied to solve the group classification problem for (1+1)-dimensional linear Schrödinger equations with complex potentials. With this technique, the problem of the group classification of the class under study is reduced to the classification of certain subalgebras of its equivalence algebra. As a result, we find that the inequivalent cases are exhausted by eight families of potentials and we give the corresponding maximal Lie invariance algebras. In the second paper we carry out the preliminary symmetry analysis of the class of linear Schrödinger equations with complex potentials in the multi-dimensional case. Using the direct method, we find the equivalence groupoid and the equivalence group of this class. Due to the multi-dimensionality, the results of the computations are quite different from the ones presented in Paper I. We obtain the complete group classification of (1+2)-dimensional linear Schrödinger equations with complex potentials.
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Hua, Jiuzhao Mathematics & Statistics Faculty of Science UNSW. "Representations of quivers over finite fields." Awarded by:University of New South Wales. Mathematics & Statistics, 1998. http://handle.unsw.edu.au/1959.4/40405.
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The main purpose of this thesis is to obtain surprising identities by counting the representations of quivers over finite fields. A classical result states that the dimension vectors of the absolutely indecomposable representations of a quiver ?? are in one-to-one correspondence with the positive roots of a root system ??, which is infinite in general. For a given dimension vector ?? ??? ??+, the number A??(??, q), which counts the isomorphism classes of the absolutely indecomposable representations of ?? of dimension ?? over the finite field Fq, turns out to be a polynomial in q with integer coefficients, which have been conjectured to be nonnegative by Kac. The main result of this thesis is a multi-variable formal identity which expresses an infinite series as a formal product indexed by ??+ which has the coefficients of various polynomials A??(??, q) as exponents. This identity turns out to be a qanalogue of the remarkable Weyl-Macdonald-Kac denominator identity modulus a conjecture of Kac, which asserts that the multiplicity of ?? is equal to the constant term of A??(??, q). An equivalent form of this conjecture is established and a partial solution is obtained. A new proof of the integrality of A??(??, q) is given. Three Maple programs have been included which enable one to calculate the polynomials A??(??, q) for quivers with at most three nodes. All sample out-prints are consistence with Kac???s conjectures. Another result of this thesis is as follows. Let A be a finite dimensional algebra over a perfect field K, M be a finitely generated indecomposable module over A ???K ??K. Then there exists a unique indecomposable module M??? over A such that M is a direct summand of M??? ???K ??K, and there exists a positive integer s such that Ms = M ??? ?? ?? ?? ??? M (s copies) has a unique minimal field of definition which is isomorphic to the centre of End ??(M???) rad (End ??(M???)). If K is a finite field, then s can be taken to be 1.
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Li, Zimu. "Fast Matrix Multiplication by Group Algebras." Digital WPI, 2018. https://digitalcommons.wpi.edu/etd-theses/131.
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Based on Cohn and Umans’ group-theoretic method, we embed matrix multiplication into several group algebras, including those of cyclic groups, dihedral groups, special linear groups and Frobenius groups. We prove that SL2(Fp) and PSL2(Fp) can realize the matrix tensor ⟨p, p, p⟩, i.e. it is possible to encode p × p matrix multiplication in the group algebra of such a group. We also find the lower bound for the order of an abelian group realizing ⟨n, n, n⟩ is n3. For Frobenius groups of the form Cq Cp, where p and q are primes, we find that the smallest admissible value of q must be in the range p4/3 ≤ q ≤ p2 − 2p + 3. We also develop an algorithm to find the smallest q for a given prime p.
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Brandt, Marco. "On unipotent Specht modules of finite general linear groups." [S.l. : s.n.], 2004. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB11103979.
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Adhikari, S. Prashanth. "Torsion in the homology of the general linear group for a ring of algebraic integers /." Thesis, Connect to this title online; UW restricted, 1997. http://hdl.handle.net/1773/5770.
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Ruether, Cameron. "Killing Forms, W-Invariants, and the Tensor Product Map." Thesis, Université d'Ottawa / University of Ottawa, 2017. http://hdl.handle.net/10393/36740.
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Associated to a split, semisimple linear algebraic group G is a group of invariant
quadratic forms, which we denote Q(G). Namely, Q(G) is the group of quadratic
forms in characters of a maximal torus which are fixed with respect to the action
of the Weyl group of G. We compute Q(G) for various examples of products of the
special linear, special orthogonal, and symplectic groups as well as for quotients of
those examples by central subgroups. Homomorphisms between these linear algebraic groups induce homomorphisms between their groups of invariant quadratic forms. Since the linear algebraic groups are semisimple, Q(G) is isomorphic to Z^n for some n, and so the induced maps can be described by a set of integers called Rost multipliers. We consider various cases of the Kronecker tensor product map between copies of the special linear, special orthogonal, and symplectic groups. We compute the Rost multipliers of the induced map in these examples, ultimately concluding that the Rost multipliers depend only on the dimensions of the underlying vector spaces.
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NOVARIO, SIMONE. "LINEAR SYSTEMS ON IRREDUCIBLE HOLOMORPHIC SYMPLECTIC MANIFOLDS." Doctoral thesis, Università degli Studi di Milano, 2021. http://hdl.handle.net/2434/886303.
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In questa tesi studiamo alcuni sistemi lineari completi associati a divisori di schemi di Hilbert di 2 punti su una superficie K3 proiettiva complessa con gruppo di Picard di rango 1, e le mappe razionali indotte. Queste varietà sono chiamate quadrati di Hilbert su superfici K3 generiche, e sono esempi di varietà irriducibili olomorfe simplettiche (varietà IHS).
Nella prima parte della tesi, usando la teoria dei reticoli, gli operatori di Nakajima e il modello di Lehn–Sorger, diamo una base per il sottospazio vettoriale dell’anello di coomologia singolare a coefficienti razionali generato dalle classi di Hodge razionali di tipo (2, 2) sul quadrato di Hilbert di una qualsiasi superficie K3 proiettiva. In seguito sfruttiamo un teorema di Qin e Wang insieme a un risultato di Ellingsrud, Göttsche e Lehn per ottenere una base del reticolo delle classi di Hodge integrali di tipo (2, 2) sul quadrato di Hilbert di una qualsiasi superficie K3 proiettiva.
Nella seconda parte della tesi studiamo il problema seguente: se X è il quadrato di Hilbert di una superficie K3 generica che ammette un divisore ampio D con q(D) = 2, dove q è la forma quadratica di Beauville-Bogomolov-Fujiki, descrivere geometricamente la mappa razionale indotta dal sistema lineare completo |D|. Il risultato principale della tesi mostra che tale X, tranne nel caso del quadrato di Hilbert di una superficie quartica generica di P^3, è una doppia EPW sestica, cioè il ricoprimento doppio di una EPW sestica, una ipersuperficie normale di P^5, ramificato nel suo luogo singolare. Inoltre la mappa razionale indotta da |D| coincide proprio con tale ricoprimento doppio. Gli strumenti principali per ottenere questo risultato sono la descrizione del reticolo delle classi integrali di Hodge di tipo (2, 2) della prima parte della tesi e l’esistenza di un’involuzione anti-simplettica su tali varietà per un teorema di Boissière, Cattaneo, Nieper-Wißkirchen e Sarti.In this thesis we study some complete linear systems associated to divisors of Hilbert schemes of 2 points on complex projective K3 surfaces with Picard group of rank 1, together with the rational maps induced. We call these varieties Hilbert squares of generic K3 surfaces, and they are examples of irreducible holomorphic symplectic (IHS) manifold. In the first part of the thesis, using lattice theory, Nakajima operators and the model of Lehn–Sorger, we give a basis for the subvector space of the singular cohomology ring with rational coefficients generated by rational Hodge classes of type (2, 2) on the Hilbert square of any projective K3 surface. We then exploit a theorem by Qin and Wang together with a result by Ellingsrud, Göttsche and Lehn to obtain a basis of the lattice of integral Hodge classes of type (2, 2) on the Hilbert square of any projective K3 surface. In the second part of the thesis we study the following problem: if X is the Hilbert square of a generic K3 surface admitting an ample divisor D with q(D)=2, where q is the Beauville–Bogomolov–Fujiki form, describe geometrically the rational map induced by the complete linear system |D|. The main result of the thesis shows that such an X, except on the case of the Hilbert square of a generic quartic surface of P^3, is a double EPW sextic, i.e., the double cover of an EPW sextic, a normal hypersurface of P^5, ramified over its singular locus. Moreover, the rational map induced by |D| is a morphism and coincides exactly with this double covering. The main tools to obtain this result are the description of integral Hodge classes of type (2, 2) of the first part of the thesis and the existence of an anti-symplectic involution on such varieties due to a theorem by Boissière, Cattaneo, Nieper-Wißkirchen and Sarti.
Dans cette thèse, nous étudions certains systèmes linéaires complets associés aux diviseurs des schémas de Hilbert de 2 points sur des surfaces K3 projectives complexes avec groupe de Picard de rang 1, et les fonctions rationnelles induites. Ces variétés sont appelées carrés de Hilbert sur des surfaces K3 génériques, et sont un exemple de variété symplectique holomorphe irréductible (variété IHS). Dans la première partie de la thèse, en utilisant la théorie des réseaux, les opérateurs de Nakajima et le modèle de Lehn–Sorger, nous donnons une base pour le sous-espace vectoriel de l’anneau de cohomologie singulière à coefficients rationnels engendré par les classes de Hodge rationnels de type (2, 2) sur le carré de Hilbert de toute surface K3 projective. Nous exploitons ensuite un théorème de Qin et Wang ainsi qu’un résultat de Ellingsrud, Göttsche et Lehn pour obtenir une base du réseau des classes de Hodge intégraux de type (2, 2) sur le carré de Hilbert d’une surface K3 projective quelconque. Dans la deuxième partie de la thèse, nous étudions le problème suivant : si X est le carré de Hilbert d’une surface K3 générique tel que X admet un diviseur ample D avec q(D) = 2, où q est la forme quadratique de Beauville–Bogomolov–Fujiki, on veut décrire géométriquement la fonction rationnelle induite par le système linéaire complet |D|. Le résultat principal de la thèse montre qu’une telle X, sauf dans le cas du carré de Hilbert d’une surface quartique générique de P^3, est une double sextique EPW, c’est-à-dire le revêtement double d’une sextique EPW, une hypersurface normale de P^5, ramifié sur son lieu singulier. En plus la fonction rationnelle induite par |D| est exactement ce revêtement double. Les outils principaux pour obtenir ce résultat sont la description des classes de Hodge intégraux de type (2, 2) de la première partie de la thèse et l’existence d’une involution anti-symplectique sur de telles variétés par un théorème de Boissière, Cattaneo, Nieper-Wißkirchen et Sarti.
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Wong, Ming Lai. "Q-Fourier transform, q-Heisenberg algebra and quantum group actions /." View Abstract or Full-Text, 2003. http://library.ust.hk/cgi/db/thesis.pl?MATH%202003%20WONG.
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Tosi, Alessandra. "Rappresentazioni lineari di SL3(C)." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2010. http://amslaurea.unibo.it/827/.
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Espongo i fatti di base della teoria delle rappresentazioni con lo scopo di indagare i possibili modi in cui un dato gruppo di Lie o algebra di Lie agisce su uno spazio vettoriale di dimensione finita. Tali risultati verranno applicati all'algebra di Lie del gruppo speciale lineare.
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Margraff, Aaron Thaddeus. "An Exposition on Group Characters." The Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1397492784.
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LANCELLOTTI, BENEDETTA. "Linear source lattices and their relevance in the representation theory of finite groups." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2018. http://hdl.handle.net/10281/199015.
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Molti dei problemi ancora aperti nella teoria delle rappresentazioni dei gruppi finiti riguardano la struttura locale-globale dei gruppi.
Sia G un gruppo finito, p un primo che ne divide l'ordine e (K,O,F) un sistema p-modulare di spezzamento. Lo studio locale-globale delle rappresentazioni di G cerca gli invarianti di G che possono essere individuati nei suoi sottogruppi locali, i.e, nel normalizzatore N di un p-sottogruppo D di G, e viceversa. Uno strumento chiave in questo contesto è la corrispondenza di Green, che stabilisce una biezione tra gli OG-reticoli indecomponibili che hanno D (o un suo coniugato in G) come vertice e gli ON-reticoli indecomponibili con vertice D.
Lo scopo principale della tesi è lo studio dei reticoli con sorgente lineare e il loro rapporto con le rappresentazioni irriducibili di G e N su K e su F. Gli oggetti principali utilizzati per questo fine sono l'anello di Grothendieck L(G) degli OG-reticoli con sorgente lineare e il suo sottoanello dei reticoli con sorgente banale.
Il primo capitolo raccoglie le definizioni e i risultati principali della teoria delle rappresentazioni utilizzati nella tesi. Una particolare attenzione è data alle proprietà dei reticoli con sorgente lineare e alla loro individuazione.
Nel Capitolo 2 sono costruite le sezioni canoniche del prodotto tensore con K (risp. con F) definito dall'anello degli OG-reticoli con sorgente lineare (risp. con sorgente banale) all'anello delle KG-rappresentazioni (risp. FG-rappresentazioni). Questo risultato è stato ottenuto seguendo due strategie. La prima prevede la costruzione di mappe duali considerando le "species" degli anelli coinvolti. Il punto di forza di questo approccio è il legame con le tavole delle rappresentazioni definite da Benson, d'altra parte però le mappe considerate prendono valori sulla complessificazione degli anelli. La seconda strategia, che risolve questo problema, consiste nell'utilizzare le formule canoniche di induzione introdotte da Boltje. Infine viene dimostrato che queste due strategie portano allo stesso risultato.
Il terzo capitolo è diviso in due parti. Nella prima viene formalmente introdotto l'anello dei reticoli essenziali con sorgente lineare, come conseguenza della definizione di opportune forme bilineari. Nella seconda parte viene analizzato il rapporto tra i reticoli con sorgente banale e vertice massimo e le KG-rappresentazioni irriducibili in due casi particolari: gruppi con sottogruppi normali di indice p e gruppi con sottogruppi di Sylow di ordine p.
Nell’ultimo capitolo viene indagato il legame tra la congettura di Alperin-McKay e il gruppo di Grothendieck Lmx(B) dei reticoli con sorgente lineare e vertice massimo in un blocco B di OG. Considerando una delle forme bilineari definite nel capitolo 3 e una opportuna sezione della proiezione canonica di L(B) in Lmx(B), è possibile formulare due nuove congetture (1 e 2), che implicano la congettura di Alperin-McKay e una sua riformulazione di Isaacs e Navarro. Inoltre la congettura 1 e la congettura di Alperin-McKay implicano la riformulazione proposta dai matematici sopracitati.
Il risultato principale di questo capitolo è la verifica della congettura 1 in alcuni casi non banali. Per esempio per blocchi "slendid equivant" al loro corrispondente di Brauer. Per un un risultato di R.Rouquier questo vale per tutti i blocchi con gruppo di difetto ciclico. In particolare, questo mostra un inedito legame tra la “splendid form” della congettura di Broué e la riformulazione di Isaacs e Navarro della congettura di Alperin-McKay.Many investigated and interesting problems in the representation theory of finite groups concern the global and local structure of the groups. Let G be a finite group, p a prime which divides the order of G and (K,O,F) a splitting p-modular system. The local-global study of the representations of G looks for the invariants of G that can be seen in its local subgroups, i.e., the normalizer N of a p-subgroup D of G, and vice versa. A very strong tool in this context is the Green correspondence, which establishes a bijection between the indecomposable OG-lattices with D as a vertex and the indecomposable ON lattices with vertex D. The main scope of this thesis is the study of linear source lattices and their connection with the irreducible representations of G and N both over K and F. The main objects involved for this goal is the Grothendieck ring of linear source OG-lattices L(G) with its subring of trivial source lattices. The first chapter is dedicated to the main results of the representation theory used through all the thesis. Special emphasis is laid on linear source lattices and their detection. In Chapter 2 the canonical sections of the surjective maps given by the tensor product with K for linear source lattices and with F for trivial source lattices are constructed. This result has been obtained following two strategies. The first involves the construction of dual maps defined considering the species of the rings. The strength of this approach is its link to the representation tables defined by Benson; but the maps constructed take values on the complexification of the rings. The canonical induction formulas introduced by R. Boltje turn out to be the solution to bypass this problem. The final result of this part is the proof that these two approaches lead to the same maps. Chapter 3 is divided in two parts. Studying a ring of modules a natural question is if it is possible to define a meaningful bilinear form. In this context the ring of essential linear source lattices arises. In the first part of Chapter 3 it is formally introduced and its species are studied. In the last part the link between trivial source lattices with maximal vertex and irreducible characters is analyzed in two particular cases: groups with normal subgroups of index p and groups with Sylow subgroups of order p. In the last chapter a connection between the Alperin-McKay conjecture and the Grothendieck group Lmx(B) of linear source lattices with maximal vertex in a block B of OG is established. Considering a bilinear form defined in Chapter 3 and a section of the canonical projection of L(B) in Lmx(B), it is possible to state two new conjectures (1 and 2). If both of them are affirmative, then they yield the Alperin-McKay conjecture and one of its refinements due to M. Isaacs and G. Navarro. Moreover, Conjecture 1 and Alperin-McKay conjecture imply its refinement stated by the previously mentioned mathematicians. The main result of this chapter is the proof of Conjecture 1 in some non trivial cases. E.g., for a block splendid equivalent to its Brauer correspondent (for some defect group) Conjecture 1 is positively verified. By a result of R. Rouquier this applies to the case of blocks with cyclic defect groups. This result establishes a new connection between the refinement due to Isaacs and Navarro and the "splendid form" of Broué conjecture.
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DI, GRAVINA LUCA MARIA. "Some questions about the Möbius function of finite linear groups." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2022. http://hdl.handle.net/10281/371474.
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La funzione di Möbius definita per insiemi parzialmente ordinati localmente finiti è un classico strumento di analisi combinatoria. Si tratta di una generalizzazione della funzione di Möbius nota in teoria dei numeri e ha varie applicazioni pure in teoria dei gruppi, dalla caratteristica di Eulero di complessi di sottogruppi fino allo studio di aspetti algebrici in automi cellulari. Nella prima parte della tesi richiamiamo alcune informazioni elementari per strutture d'ordine che sono legate alla funzione di Möbius, e ne presentiamo le principali proprietà, quali ad esempio la formula di inversione di Möbius e i teoremi di Crapo. Inoltre analizziamo alcuni legami importanti con argomenti di teoria dei gruppi, al fine di motivare il nostro interesse nei confronti della funzione di Möbius di gruppi lineari finiti. Nella seconda parte, lavoriamo su questi gruppi per studiarne la funzione di Möbius e otteniamo risultati originali che si rivelano utili per calcolarla, nota la struttura di alcuni particolari reticoli di sottospazi associati ai sottogruppi. Vediamo in dettaglio il caso in cui abbiamo un reticolo di sottospazi distributivo. In seguito mostriamo un esempio di sottogruppo del gruppo lineare generale, tale che il reticolo di sottospazi associato al sottogruppo non è distributivo. In questo modo osserviamo che i nostri ragionamenti hanno una validità più ampia e possono essere applicati a situazioni differenti, sotto determinate condizioni. Nell'ultima parte della tesi, colleghiamo i risultati ottenuti in precedenza ad alcune questioni aperte che riguardano gruppi profiniti finitamente generati e gruppi finiti almost-simple, presentando un approccio originale al problema. Benché poi questo problema non venga completamente risolto, otteniamo degli utili risultati parziali che possono essere sviluppati in futuro.The Möbius function of locally finite partially ordered sets is a classical tool in enumerative combinatorics. It is a generalization of the number-theoretic Möbius function and it has several applications in group theory, from the Euler characteristic of subgroup complexes to algebraic aspects of cellular automata. In the first part of the thesis, we recall some basic notions about the order structures which are related to the Möbius function, and we present its main properties, such as the Möbius inversion formula and Crapo's theorems. Moreover, we investigate some relevant connections with group-theoretical topics to motivate our interest in the Möbius function of finite linear groups. In the second part, we work on these groups to obtain information about their Möbius function, and our original results are useful to compute it if we know the structure of some special subspace lattices related to subgroups. We study in detail the case of distributive subspace lattices. Then we show an example of a subgroup in the general linear group, such that the subspace lattice associated to the subgroup is non-distributive. In this way, we see that our arguments can also be applied to different situations, under certain conditions. In the last part of the thesis, we connect the previously obtained results to an open question about finitely generated profinite groups and finite almost-simple groups, introducing an original approach to the problem. Although we do not completely answer to this last question, we get some useful partial results.
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Guin, Daniel. "Homologie du groupe lineaire et symboles en k-theorie algebrique." Université Louis Pasteur (Strasbourg) (1971-2008), 1987. http://www.theses.fr/1987STR13055.
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On etablit, pour une large classe d'anneaux non necessairement communicatifs, un resultat de stabilite de l'homologie du groupe lineaire. On donne une presentation par generateurs et relations de premiere obstruction a cette stabilite. On obtient ainsi une generalisation aux anneaux de la k-theorie de milnor. On developpe ensuite une theorie d'homologie et de cohomologie non abeliennes des groupes. Cette theorie permet une comparaison, en basse dimension, des k-theories de quillen et de milnor, d'un anneau non communicatif. On etudie ensuite l'existence d'une suite exacte de localisation pour la k-theorie de milnor
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Gardiner, Christopher James. "Quasiconformal maps on a 2-step Carnot group." Bowling Green State University / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1498487423057279.
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BORELLO, MARTINO. "Automorphism groups of self-dual binary linear codes with a particular regard to the extremal case of length 72." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2014. http://hdl.handle.net/10281/49887.
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Let C be a binary linear code and suppose that its automorphism
group contains a non trivial subgroup G. What can we say about C knowing
G? In this thesis we collect some answers to this question. We focus on the cases G = C_p, G = C_2p and G = D_2p (p an odd prime), with a particular regard to the case in which C is self-dual. Furthermore we generalize some methods used in other papers on this subject. The third chapter is devoted to the investigation of the automorphism group of a putative self-dual [72; 36; 16] code, whose existence is a long-standing open problem. Last chapter is about semi self-dual codes and new upped bound on their dual distance.
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Roman, Ahmed Hemdan. "Zero Divisors and Linear Independence of Translates." Thesis, Virginia Tech, 2015. http://hdl.handle.net/10919/53956.
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In this thesis we discuss linear dependence of translations which is intimately related to the zero divisor conjecture. We also discuss
the square integrable representations of the generalized Wyle-Heisenberg group in $n^2$ dimensions and its relations with Gabor's question
from Gabor Analysis in the light of the time-frequency equation. We study the zero divisor conjecture in relation to
the reduced $C^*$-algebras and operator norm $C^*$-algebras. For certain classes of groups we address the zero divisor conjecture by providing
an isomorphism between the the reduced $C^*$-algebra and the operator norm $C^*$-algebra. We also provide an isomorphism between the algebra of weak closure and the von Neumann algebra under mild conditions. Finally, we prove some theorems
about the injectivity of some spaces as $mathbb{C}G$ modules for some groups $G$.Master of Science
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Wyles, Stacie Nicole. "Doubly-Invariant Subgroups for p=3." University of Akron / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=akron1428336632.
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Barnes, Sue. "Aspects of the ring of invariants of the orthogonal group over finite fields in odd characteristic." Thesis, University of Glasgow, 2008. http://theses.gla.ac.uk/300/.
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Let $V$ be a non-zero finite dimensional vector space over a finite field $\mathbb{F}_q$ of odd characteristic. Fixing a non-singular quadratic form $\xi_0$ in $S^2(V^*)$, the symmetric square of the dual of V we are concerned with the Orthogonal group $O(\xi_0)$, the subgroup of the General Linear Group $GL(V)$ that fixes $\xi_0$ and with invariants of this group. We have the Dickson Invariants which being invariants of the General Linear Group are then invariants of $O(\xi_0)$. Considering the $O(\xi_0)$ orbits of the dual vector space $\vs$ we generate the Chern Orbit polynomials, the coefficients of which, the Chern Orbit Classes, are also invariants of the Orthogonal group. The invariants $\xi_1, \xi_2, \dots $ are be generated from $\xi_0$ by applying the action of the Steenrod Algebra to $S^2(V^*)$ which being natural takes invariants to invariants. Our aim is to discover further invariants from these known invariants with the intention of establishing a set of generators for the the Ring of invariants of the Orthogonal Group. In particular we calculate invariants of $O(\xi_0)$ when the dimension of the vector space is $4$ the finite field is $\mathbb{F}_3$ and the quadratic form is $\xi_0=x_1^2+x_2^2+x_3^2+x_4^2$ and we are able to establish an explicit presentation of $O(\xi_0)$ in this case.
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Marzouki, Mohamed Amine. "Group-theoretical investigation of the structural basis for the formation of twinned crystals." Thesis, Université de Lorraine, 2015. http://www.theses.fr/2015LORR0102/document.
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Le travail de cette thèse porte sur les raisons structurales derrière la formation de cristaux maclés. Ce travail ouvre une voie pour un futur développement de protocoles de synthèse afin de réduire l'occurrence de macles. La motivation de cette étude est que la présence de macles affecte négativement les propriétés physico-chimiques des matériaux d'intérêts technologiques et réduit aussi la qualité des données expérimentales sur lesquelles se fonde l'analyse structurelle. Ce dernier problème est particulièrement sensible dans le cas de cristaux ayant des paramètres de maille importantes, comme les macromolécules biologiques. Les principes de symétrie responsables du phénomène de maclage dans le cas d’une macle de transformation ou d'origine mécanique sont bien connues. En revanche dans le cas d’une macle de croissance, le maclage est toujours considéré comme un accident lié aux conditions aléatoires de croissance cristalline où à la cinétique, plutôt qu'à la thermodynamique. Une approche générale connue comme la « théorie réticulaire des macles » a été développée depuis le XIXe siècle, fondée sur l'existence d'un sous-réseau commun aux cristaux maclés, qui donne les conditions nécessaires pour l'apparition d'une macle. Cette approche est cependant insuffisante pour déterminer la différence entre les macles avec le même degré de chevauchement des réseaux mais montrant une fréquence d'occurrence assez différente. Une approche structurale, fondée sur l'analyse de la symétrie propre des orbites cristallographiques a été proposée il y a plus d'un demi-siècle (Donnay et Curien, 1960), mais est restée à l'état embryonnaire, malgré une certaine reprise récente (Nespolo et Ferraris, 2009). En outre, l'idée qu'une interface commune aux cristaux maclés puisse contenir une opération reliant ces individus a été proposée (Holser, 1958) mais n'a jamais été portée à un plein développement. Dans cette thèse, nous présentons un développement algébrique de ces idées. Nous montrons que les conditions structurales nécessaires pour la formation d'une macle de croissance peuvent être formulées en se basant, notamment, sur la symétrie propre des orbites cristallographiques et sur le groupe sous-périodique de la couche transversale donnant la symétrie d'une couche commune. L'analyse détaillée dans cette thèse de trois macles fréquentes démontre une corrélation claire entre le degré de restauration de la structure par l'opération de maclage et la fréquence d'occurrence des macles. Un exemple négatif, à savoir une macle hypothétique dont on pourrait prévoir la formation sur la base de la théorie réticulaire a aussi été analysé. Le fait que cette macle n'ait jamais été observée, en raison d’une faible restauration de la structure qui serait produite par l'opération de macle, confirme le bien fondé de l'approche. Nous nous attendons à ce que la généralisation de l'approche présentée dans cette thèse fournisse une procédure semi-automatique pour prévoir la probabilité de formation d'une macle. Cela permettrait aux personnes travaillant dans la synthèse cristalline démoduler la fréquence de maclage. Le procédé fait appel à la modification de la morphologie du cristal pour une plus grande exposition et le développement des faces cristallines qui présentent une interface défavorable pour le maclageThis thesis addresses the structural rationale behind the formation of growth twins, with the purpose of opening a route to the future development of synthesis protocols to reduce the occurrence frequency of twinning. The reason for this effort is that twinning affects negatively the physico-chemical properties of materials and biomaterials of technological interests and reduces the quality of the experimental data on which the structural investigation is based. While on the one hand the reasons for twinning in transformation and mechanical twins are well understood, in the case of growth twins twinning is still seen as an accident linked to aleatory conditions where kinetics, rather than thermodynamics, plays a principal role. A general approach known as the reticular theory of twinning has been developed since the XIX century, based on the existence of a sublattice common to the twinned crystals, which gives the minimal necessary conditions for the occurrence of a twin. This approach is, however, insufficient to discriminate between twins with the same degree of lattice overlap but showing a fairly different occurrence frequency. A structural approach, based on the analysis of the eigensymmetry of the crystallographic orbits building a crystal structure was proposed more than half a century ago (Donnay and Curien, 1960) but remained at an embryonic state, despite some recent revival (Nespolo and Ferraris, 2009). Also, the idea that a slice common to the twinned individuals may contain an operation mapping these individuals was proposed (Holser, 1958) but never brought to a full development. In this thesis, we present a full development of these ideas and show that the structurally necessary conditions for the formation of a growth twin can be described on the basis of the eigensymmetry of the crystallographic orbits and on the sectional layer group giving the symmetry of the common slice. The detailed analysis of three well-know twins demonstrates a clear correlation between the degree of structural restoration by the twin operation and the occurrence frequency of the twins. The analysis of a negative example, i.e. of a hypothetical twin which one would expect on the basis of the reticular theory but has never been observed, strengthens the evidence of this correlation, because of the low structural restoration one would observe in that twin. We expect that the generalisation of the approach presented in this thesis through a semi-automatic procedure will provide crystal growers with a powerful tool to modulate the occurrence frequency of twinning through a modification of the crystal morphologies towards a larger exposure and development of crystal faces which represent an unfavorable interface for twinning
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Altafi, Nasrin. "Lefschetz Properties of Monomial Ideals." Licentiate thesis, KTH, Matematik (Inst.), 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-223373.
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This thesis concerns the study of the Lefschetz properties of artinian monomial algebras. An artinian algebra is said to satisfy the strong Lefschetz property if multiplication by all powers of a general linear form has maximal rank in every degree. If it holds for the first power it is said to have the weak Lefschetz property (WLP). In the first paper, we study the Lefschetz properties of monomial algebras by studying their minimal free resolutions. In particular, we give an afirmative answer to an specific case of a conjecture by Eisenbud, Huneke and Ulrich for algebras having almost linear resolutions. Since many algebras are expected to have the Lefschetz properties, studying algebras failing the Lefschetz properties is of a great interest. In the second paper, we provide sharp lower bounds for the number of generators of monomial ideals failing the WLP extending a result by Mezzetti and Miró-Roig which provides upper bounds for such ideals. In the second paper, we also study the WLP of ideals generated by forms of a certain degree invariant under an action of a cyclic group. We give a complete classication of such ideals satisfying the WLP in terms of the representation of the group generalizing a result by Mezzetti and Miró-Roig.QC 20180220
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Floderová, Hana. "Geometrické struktury založené na kvaternionech." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2010. http://www.nusl.cz/ntk/nusl-229021.
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A pair (V, G) is called geometric structure, where V is a vector space and G is a subgroup GL(V), which is a set of transmission matrices. In this thesis we classify structures, which are based on properties of quaternions. Geometric structures based on quaternions are called triple structures. Triple structures are four structures with similar properties as quaternions. Quaternions are generated from real numbers and three complex units. We write quaternions in this shape a+bi+cj+dk.
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Frazier, William. "Application of Symplectic Integration on a Dynamical System." Digital Commons @ East Tennessee State University, 2017. https://dc.etsu.edu/etd/3213.
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Molecular Dynamics (MD) is the numerical simulation of a large system of interacting molecules, and one of the key components of a MD simulation is the numerical estimation of the solutions to a system of nonlinear differential equations. Such systems are very sensitive to discretization and round-off error, and correspondingly, standard techniques such as Runge-Kutta methods can lead to poor results. However, MD systems are conservative, which means that we can use Hamiltonian mechanics and symplectic transformations (also known as canonical transformations) in analyzing and approximating solutions. This is standard in MD applications, leading to numerical techniques known as symplectic integrators, and often, these techniques are developed for well-understood Hamiltonian systems such as Hill’s lunar equation. In this presentation, we explore how well symplectic techniques developed for well-understood systems (specifically, Hill’s Lunar equation) address discretization errors in MD systems which fail for one or more reasons.
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Ovchinnikov, Alexey I. "Tannakian categories and linear differential algebraic groups." 2007. http://www.lib.ncsu.edu/theses/available/etd-02222007-114103/unrestricted/etd.pdf.
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Carmody, Michael. "Linear algebraic groups, with special emphasis on the classical groups." Master's thesis, 2009. http://hdl.handle.net/1885/148268.
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"Unitary representations of general linear groups." Chinese University of Hong Kong, 1985. http://library.cuhk.edu.hk/record=b5885572.
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Basheer, Ayoub Basheer Mohammed. "Character tables of the general linear group and some of its subgroups." Thesis, 2008. http://hdl.handle.net/10413/978.
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The aim of this dissertation is to describe the conjugacy classes and some of the ordinary irreducible characters of the nite general linear group GL(n, q); together with character tables of some of its subgroups. We study the structure of GL(n, q) and some of its important subgroups such as SL(n, q); UT(n, q); SUT(n, q); Z(GL(n, q)); Z(SL(n, q)); GL(n, q)0 ; SL(n, q)0 ; the Weyl group W and parabolic subgroups P : In addition, we also discuss the groups PGL(n, q); PSL(n, q) and the a ne group A (n, q); which are related to GL(n, q): The character tables of GL(2; q); SL(2; q); SUT(2; q) and UT(2; q) are constructed in this dissertation and examples in each case for q = 3 and q = 4 are supplied. A complete description for the conjugacy classes of GL(n, q) is given, where the theories of irreducible polynomials and partitions of i 2 f1; 2; ; ng form the atoms from where each conjugacy class of GL(n, q) is constructed. We give a special attention to some elements of GL(n, q); known as regular semisimple, where we count the number and orders of these elements. As an example we compute the conjugacy classes of GL(3; q): Characters of GL(n, q) appear in two series namely, principal and discrete series characters. The process of the parabolic induction is used to construct a large number of irreducible characters of GL(n, q) from characters of GL(n, q) for m < n: We study some particular characters such as Steinberg characters and cuspidal characters (characters of the discrete series). The latter ones are of particular interest since they form the atoms from where each character of GL(n, q) is constructed. These characters are parameterized in terms of the Galois orbits of non-decomposable characters of F
q n: The values of the cuspidal characters on classes of GL(n, q) will be computed. We describe and list the full character table of GL(n, q):
There exists a duality between the irreducible characters and conjugacy classes of GL(n, q); that is to each irreducible character, one can associate a conjugacy class of GL(n, q): Some aspects of this duality will be mentioned.Thesis (M.Sc. (School of Mathematical Sciences)) - University of KwaZulu-Natal, Pietermaritzburg, 2008.
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"Morita equivalence and isomorphisms between general linear groups." Chinese University of Hong Kong, 1994. http://library.cuhk.edu.hk/record=b5888249.
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by Lok Tsan-ming.Thesis (M.Phil.)--Chinese University of Hong Kong, 1994.
Includes bibliographical references (leaves 74-75).
Introduction --- p.2
Chapter 1 --- "Rings, Modules and Categories" --- p.4
Chapter 1.1 --- "Rings, Subrings and Ideals" --- p.5
Chapter 1.2 --- Modules and Categories --- p.8
Chapter 1.3 --- Module Theory --- p.13
Chapter 2 --- Isomorphisms between Endomorphism rings of Quasiprogener- ators --- p.24
Chapter 2.1 --- Preliminaries --- p.24
Chapter 2.2 --- The Fundamental Theorem --- p.31
Chapter 2.3 --- Isomorphisms Induced by Semilinear Maps --- p.41
Chapter 2.4 --- Isomorphisms of General linear groups --- p.46
Chapter 3 --- Endomorphism ring of projective module --- p.54
Chapter 3.1 --- Preliminaries --- p.54
Chapter 3.2 --- Main Theorem --- p.60
Bibliography --- p.74
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Van, Alten Clint Johann. "An algebraic study of residuated ordered monoids and logics without exchange and contraction." Thesis, 1998. http://hdl.handle.net/10413/3961.
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Ryan, Philip D. "Some examples in the Bruhat order on symmetric varieties." Master's thesis, 1991. http://hdl.handle.net/1885/139515.
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Pekker, Alexander. "Dirichlet's Theorem in projective general linear groups and the Absolute Siegel's Lemma." Thesis, 2006. http://hdl.handle.net/2152/2789.
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Bapela, Manas Majakwane. "Riesz theory and Fredholm determinants in Banach algebras." Thesis, 1999. http://hdl.handle.net/2263/30088.
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In the classical theory of operators on a Banach space a beautiful interplay exists between Riesz and Fredholm theory, and the theory of traces and de¬terminants for operator ideals. In this thesis we obtain a complete Riesz de¬composition theorem for Riesz elements in a semi prime Banach algebra and on the other hand extend the existing theory of traces and determinants to a more general setting of Banach algebras. In order to obtain some of these results we use the notion of finite multiplicity of spectral points to give a characterization of the essential spec¬trum for elements in a Banach algebra. As an immediate corollary we obtain the well-known characterization of Riesz elements namely that their non-zero spectral points are isolated and of finite multiplicities. In the final chapter of the thesis we use Plemelj's type formulas to define a determinant on the ideal of finite rank elements and show that it extends continuously to the ideal of nuclear elements.Thesis (PhD (Mathematics))--University of Pretoria, 2006.
Mathematics and Applied Mathematics
unrestricted
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Seçkin, Elif. "Centralizers of elements of prime order in locally finite simple groups." Diss., 2008.
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Ondrus, Alexander A. "Minimal anisotropic groups of higher real rank." Phd thesis, 2010. http://hdl.handle.net/10048/1001.
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Thesis (Ph. D.)--University of Alberta, 2010.Title from pdf file main screen (viewed on June 24, 2010). A thesis submitted to the Faculty of Graduate Studies and Research in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mathematics, [Department of] Mathematical and Statistical Sciences, University of Alberta. Includes bibliographical references.