Dissertations / Theses: 'Lie group'

1

pl, tomasz@uci agh edu. "A Lie Group Structure on Strict Groups." ESI preprints, 2001. ftp://ftp.esi.ac.at/pub/Preprints/esi1076.ps.

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Harkins, Andrew. "Combining lattices of soluble lie groups." Thesis, University of Newcastle Upon Tyne, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.341777.

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Belliart, Michel. "Actions de groupes de Lie sur les variétés compactes." Valenciennes, 1995. https://ged.uphf.fr/nuxeo/site/esupversions/9806b24c-e64d-4e28-b75a-6d3de2b5eb3a.

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Cette thèse est en deux parties. Dans la première partie, on énonce, justifie et montre partiellement la conjecture suivante : L'action localement libre de codimension 1, au moins deux fois continument différentiable et préservant le volume d'un groupe de Lie non-unimodulaire sur une variété compacte est conjuguée dans sa classe de différentiabilité à une action homogène. On fournit également des exemples de groupes auxquels ce résultat s'applique. Dans la seconde partie, on répond complètement au problème suivant, posé par J. F. Plante en 1986 : A quelles conditions un groupe de Lie connexe donné peut-il agir continument et sans point fixe global sur une surface compacte donnée ? On en déduit une réponse à trois questions posées par Plante dans le même domaine. Ces deux résultats constituent la partie originale de la thèse. Ils sont précédés de deux survols, l'un de la théorie de Lie, l'autre de celle des surfaces, et la seconde partie est suivie d'une copie du dernier chapitre de la thèse de Mostow, ce qui en facilite la lecture.

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4

Lupi, Giulia. "Kernel approximations in Lie groups and application to group-invariant CNN." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/23905/.

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In questa tesi viene studiata un'equazione di convezione-diffusione-erosione introdotta in problemi di image processing. In particolare, si cercano approssimazioni dei nuclei per l'equazione di diffusione e per l'equazione di erosione. Per fare tali approssimazioni si é utilizzato il metodo della parametrice per l'equazione di diffusione, mentre il nucleo dell'equazione di erosione viene trovato a partire dal nucleo dell'equazione di diffusione attraverso la trasformata di Cramér-Fuorier.

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5

Niederkrüger, Klaus. "Compact Lie group actions on contact manifolds." [S.l. : s.n.], 2005. http://deposit.ddb.de/cgi-bin/dokserv?idn=975890360.

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6

Shingel, Tatiana. "Structured approximation in a lie group setting." Thesis, University of Cambridge, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.611555.

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7

Sandfeldt, Sven. "Local Rigidity of Some Lie Group Actions." Thesis, KTH, Matematik (Avd.), 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-272842.

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In this paper we study local rigidity of actions of simply connected Lie groups. In particular, we apply the Nash-Moser inverse function theorem to give sufficient conditions for the action of a simply connected Lie group to be locally rigid. Let $G$ be a Lie group, $H < G$ a simply connected subgroup and $\Gamma < G$ a cocompact lattice. We apply the result for general actions of simply connected groups to obtain sufficient conditions for the action of $H$ on $\Gamma\backslash G$ by right translations to be locally rigid. We also discuss some possible applications of this sufficient condition
I den här texten så studerar vi lokal rigiditet av gruppverkan av enkelt sammanhängande Liegrupper. Mer specifikt, vi applicerar Nash-Mosers inversa funktionssats för att ge tillräckliga villkor för att en gruppverkan av en enkelt sammanhängande grupp ska vara lokalt rigid. Låt $G$ vara en Lie grupp, $H < G$ en enkelt sammanhängande delgrupp och $\Gamma < G$ ett kokompakt gitter. Vi applicerar resultatet för generella gruppverkan av enkelt sammanhängande grupper för att få tillräckliga villkor för att verkan av $H$ på $\Gamma\backslash G$ med translationer ska vara lokalt rigid. Vi diskuterar också några möjliga tillämpningar av det tillräckliga villkoret.

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8

Karki, Manoj Babu. "Invariant Riemannain metrics on four-dimensional Lie group." University of Toledo / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1438906778.

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9

Sale, Andrew W. "The length of conjugators in solvable groups and lattices of semisimple Lie groups." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:ea21dab2-2da1-406a-bd4f-5457ab02a011.

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The conjugacy length function of a group Γ determines, for a given a pair of conjugate elements u,v ∈ Γ, an upper bound for the shortest γ in Γ such that uγ = γv, relative to the lengths of u and v. This thesis focuses on estimating the conjugacy length function in certain finitely generated groups. We first look at a collection of solvable groups. We see how the lamplighter groups have a linear conjugacy length function; we find a cubic upper bound for free solvable groups; for solvable Baumslag--Solitar groups it is linear, while for a larger family of abelian-by-cyclic groups we get either a linear or exponential upper bound; also we show that for certain polycyclic metabelian groups it is at most exponential. We also investigate how taking a wreath product effects conjugacy length, as well as other group extensions. The Magnus embedding is an important tool in the study of free solvable groups. It embeds a free solvable group into a wreath product of a free abelian group and a free solvable group of shorter derived length. Within this thesis we show that the Magnus embedding is a quasi-isometric embedding. This result is not only used for obtaining an upper bound on the conjugacy length function of free solvable groups, but also for giving a lower bound for their L_p compression exponents. Conjugacy length is also studied between certain types of elements in lattices of higher-rank semisimple real Lie groups. In particular we obtain linear upper bounds for the length of a conjugator from the ambient Lie group within certain families of real hyperbolic elements and unipotent elements. For the former we use the geometry of the associated symmetric space, while for the latter algebraic techniques are employed.

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Giroux, Yves. "Degenerate enveloping algebras of low-rank groups." Thesis, McGill University, 1986. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=74026.

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11

Berland, Håvard. "Lie group and exponential integrators: Theory, implementation, and applications." Doctoral thesis, Norwegian University of Science and Technology, Department of Mathematical Sciences, 2006. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-1808.

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This PhD-thesis contains an introduction and six research papers sorted chronologically, of which the first four are accepted for publication. The introduction aims at giving a very brief summary of the background theory needed for the following papers. Also, some motivation of the issues addressed by the papers is given. Paper I discusses algebraic structures of ordered rooted trees and their applications to Lie group integrators. Results from Hopf algebra theory on elementary differentials for Lie group integrators are used, and applications to order analysis and backward error analysis are given. Paper II, III, IV, and V are primarily on exponential integrators, a class of numerical schemes tailored the solution of stiff systems of systems of ordinary differential equations. Paper II discusses classical order analysis and gives some theoretical results on the form of the integrators, applicable for the construction of high order exponential integrators. Paper III is on an implementation of exponential integrators on computers, and source code, available electronically, accompanies the paper. Paper IV includes an analytical and numerical study of the performance of two classes of exponential integrators on the nonlinear Schrödinger equation. Paper V is a numerical study of behaviour over long integration invervals on the nonlinear Schrödinger equation, using nonlinear spectral theory for determining validity of the numerical solution and thereby jugdging the numerical integrators. At last, in Paper VI, properties of a class of exponential like functions, essential in exponential integrators, are derived, using an approach based on Lie group theory.

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12

Hunter, Brian. "Shared control for teleoperation using a Lie group approach." Thesis, University College London (University of London), 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.244584.

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Shared control is a technique to provide interactive autonomy in a telerobotic task, replacing the requirement for pure teleoperation where the operator's intervention is unnecessary or even undesirable. In this thesis, a geometrically correct theory of shared control for teleoperation is developed using differential geometry. The autonomous function proposed is force control. In shared control, the workspace is commonly partitioned into a "position domain" and a "force domain". This computational process requires the use of a metric. In the context of manifolds, these are known as Riemannian metrics. The switching matrix is shown to be equivalent to a filter which embodies a Riemannian metric form. However, since the metric form is non-invariant, it is shown that the metric form must undergo a transformation if the measurement reference frame is moved. If the transformation is not made, then the switching matrix fails to produce correct results in the new measurement frame. Alternatively, the switching matrix can be viewed as a misinterpretation of a projection operator. Again, the projection operator needs to be transformed correctly if the measurement reference frame is moved. Many robot control architectures preclude the implementation of robust force control. However, a compliant device mounted between the robot wrist and the workpiece can be a good alternative in lieu of explicit force control. In this form of shared control, force and displacement are regulated by control of displacement only. The geometry of compliant devices is examined in the context of shared control and a geometrically correct scheme for shared control is derived. This scheme follows naturally from a theoretical analysis of stiffness and potential energy. This thesis unifies some recent results formulated for robotic hybrid position / force control under the modern framework of differential geometry and Lie groups.

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13

Arenas, Ruben. "Constructing a Matrix Representation of the Lie Group G2." Scholarship @ Claremont, 2005. https://scholarship.claremont.edu/hmc_theses/166.

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We define the Lie group G2 and show several equivalent ways to view G2. We do the same with its Lie algebra g2. We identify a new basis for g2 using Bryant’s view of g2 and geometric considerations we develop. We then show how to construct a matrix representation of G2 given our particular basis for g2. We examine the geometry of 1 and 2-parameter subgroups of G2. Finally, we suggest an area of further research using the new geometric characterization we developed for g2.

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14

Chung, Kin Hoong School of Mathematics UNSW. "Compact Group Actions and Harmonic Analysis." Awarded by:University of New South Wales. School of Mathematics, 2000. http://handle.unsw.edu.au/1959.4/17639.

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A large part of the structure of the objects in the theory of Dooley and Wildberger [Funktsional. Anal. I Prilozhen. 27 (1993), no. 1, 25-32] and that of Rouviere [Compositio Math. 73 (1990), no. 3, 241-270] can be described by considering a connected, finite-dimentional symmetric space G/H (as defined by Rouviere), with ???exponential map???, Exp, from L G/L H to G/H, an action, ???: K ??? Aut??(G) (where Aut?? (G) is the projection onto G/H of all the automorphisms of G which leave H invariant), of a Lie group, K, on G/H and the corresponding action, ???# , of K on L G/L H defined by g ??? L (???g), along with a quadruple (s, E, j, E#), where s is a ???# - invariant, open neighbourhood of 0 in L G/L H, E is a test-function subspace of C??? (Exp s), j ?? C??? (s), and E# is a test-function subspace of C??? (s) which contains { j.f Exp: f ?? E }. Of interest is the question: Is the function ???: ?? ??? ????, where ??: f ??? j.f Exp, a local associative algebra homomorphism from F# with multiplication defined via convolution with respect to a function e: s x s ??? C, to F, with the usual convolution for its multiplication (where F is the space of all ??? - invariant distributions of E and F# is the space of all ???# - invariant distributions of E#)? For this system of objects, we can show that, to some extent, the choice of the function j is not critical, for it can be ???absorbed??? into the function e. Also, when K is compact, we can show that ??? ker ?? = { f ?? E : ???k f (???g) dg = 0}. These results turn out to be very useful for calculations on s2 ??? G/H, where G = SO(3) and H??? SO(3) with H ??? SO(2) with ??? : h ??? Lh, as we can use these results to show that there is no quadruple (s, E, j, E#) for SO(3)/H with j analytic in some neighbourhood of 0 such that ??? is a local homomorphism from F# to F. Moreover, we can show that there is more than one solution for the case where s, E and E# are as chosen by Rouviere, if e is does not have to satisfy e(??,??) = e(??,??).

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15

Otieno, Andrew Alex Omondi. "Application of lie group analysis to mathematical models in epidemiology." Thesis, Walter Sisulu University, 2013. http://hdl.handle.net/11260/100.

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Lie group analysis is arguably the most systematic vehicle for finding exact solutions of differential equations. Using this approach one has at one's disposal a variety of algorithms that make the solution process of many differential equations algorithmic. Vital properties of a given differential equation can often be inferred from the symmetries admitted by the equation. However, Lie group analysis has not enjoyed wide-spread application to systems of first-order ordinary differential equations. This is because such systems typically admit an infinite number of Lie point symmetries, and there is no systematic way to find even a single nontrivial one-dimensional Lie symmetry algebra. In the few applications available, the approach has been to circumvent the problem by transforming a given system of first-order ordinary differential equations into one in which at least one of the equations is of order two or greater. It is therefore fair to say that the full power of Lie group analysis has not been sufficiently harnessed in the solution of systems of first-order ordinary differential equations. In this dissertation we review some applications of Lie group analysis to systems of first order ordinary differential equations. We shed light on the integration procedure for first-order systems of ordinary differential equations admitting a solvable Lie algebra. We do this via instructive examples drawn from mathematical epidemiology models. In particular we revisit the work of Nucci and Torrisi [54] and improve the exposition of the Lie-symmetry-inspired solution of a mathematical model which describes a HIV transmission. To aid implementation of the integration strategy for systems of ordinary differential equations, we have developed ad-hoc routines for finding particular types of admitted symmetries and checking if a given symmetry is indeed admitted by a system of ordinary differential equations.

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16

Lindman, Hornlund Josef. "Sigma-models and Lie group symmetries in theories of gravity." Doctoral thesis, Universite Libre de Bruxelles, 2011. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209911.

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En utilisant des modèles sigma non-linéaires de fonctions d'un espace-temps D-dimensionnel à un espace symétrique G/H, nous discutons de solutions de type trou noir et membrane noire dans diverses théories de gravité supersymétriques. Un espace symétrique est une variété, riemannienne ou pseudo-riemannienne, pour laquelle le tenseur de Riemann est covariantement constant. L'utilisation du dictionnaire Kac-Moody/supergravité et les techniques de réduction dimensionnelles nous permettent de décrire des trous noirs de cohomogénéité un comme des géodésiques sur G/H. Un espace-temps M, potentiellement agrémenté d'un trou noir, est de cohomogénéité un s'il existe un groupe d'isométries Iso qui agit sur M et dont le quotient M/Iso est uni-dimensionnel. L'utilisation d'algèbres de Kac-Moody dans les théories de gravité a été développé dans l'espoir de décourvrir la symétrie sous-jacente de la théorie des cordes, aussi appelée théorie M. Les techniques de réduction dimensionnelle ont depuis longtemps été utilisées pour dévoiler les symétries cachées des théories de gravité. Dans la description du modèle sigma, les trous noirs extrémaux ou branes noires sont des géodésiques nulles et correspondent à un élément nilpotent de l'algèbre de Lie g de G. Un élément X nilpotent est caractérisé par la propriété X^n = 0. En utilisant le formalisme mathématique decrivant les orbites nilpotentes, nous classifions tous les trous noirs extrémaux dans la supergravité N=2 minimale à quatre dimensions, N=2 S^3 supergravité en quatre dimensions et la supergravité minimale en cinq dimensions. De la même manière, quand G est un sous-groupe d'un groupe Kac-Moody, très-étendu ou sur-étendu, on envoie l'orbite nilpotente minimale, en utilisant le plus haut poids de g, sur des solutions supersymétriques et non-supersymétriques de type brane dans les théories de supergravité à dix et onze dimensions. Nos résultats montrent que les symétries du groupe de Lie sont très utiles de ces solutions pour classer et trouver de nouvelles solutions de type trou noir. Afin de prouver l'unicité et plusieurs autres résultats formels, nous avons développé des méthodes préliminaires dans l'espoir qu'elles puissent être utilisées à l'avenir pour l'étude des trous noirs.
Doctorat en Sciences
info:eu-repo/semantics/nonPublished

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17

Pietraho, Thomas 1973. "Orbital varieties and unipotent representations of classical semisimple Lie group." Thesis, Massachusetts Institute of Technology, 2001. http://hdl.handle.net/1721.1/8672.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2001.
Includes bibliographical references (p. 81-83).
Let G be a complex semi-simple and classical Lie group. The notion of a Lagrangian covering can be used to extend the method of polarizing a nilpotent coadjoint orbit to obtain a unitary representation of G. W. Graham and D. Vogan propose such a construction, relying on the notions of orbital varieties and admissible orbit data. The first part of the thesis seeks to understand the set of orbital varieties contained in a given nipotent orbit. Starting from N. Spaltenstein's parameterization of the irreducible components of the variety of flags fixed by a unipotent, we produce a parameterization of the orbital varieties lying in the corresponding fiber of the Steinberg map. The parameter set is the family of standard Young or domino tableau of a given shape. The key to the proof is understanding certain closed cycles as defined by D. Garfinkle. This parameterization is particularly useful; it provides a method of determining the r-invariant of each orbital variety, as well as a way of relating an orbital variety in any classical group to one lying in type A.
(cont.) The second part of the thesis addresses the representations V(V, ir) constructed by Graham and Vogan. A natural question is how well the V(V, 7r) approximate the set of unipotent representations that ought to be attached to the nilpotent orbit 0. The answer is promising in the setting of spherical orbits. When it is possible to carry out the Graham-Vogan construction, the corresponding infinitesimal character lies in the set of characters suggested by W. M. McGovern. Furthermore, we show that it is possible to carry out the Graham-Vogan construction for a suffient number of orbital varieties to account for all the infinitesimal characters attached to 0 by McGovern.
by Thomas Pietraho.
Ph.D.

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18

Budde, Julia [Verfasser]. "Wave front sets of nilpotent lie group representations / Julia Budde." Paderborn : Universitätsbibliothek, 2021. http://d-nb.info/122950415X/34.

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19

Nakagawa, Masaki. "The space of loops on the exceptional Lie group E6." 京都大学 (Kyoto University), 2002. http://hdl.handle.net/2433/150075.

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20

Hindeleh, Firas Y. "Tangent and Cotangent Bundles, Automorphism Groups and Representations of Lie Groups." University of Toledo / OhioLINK, 2006. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1153933389.

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21

Stefanicki, Tomasz. "On subalgebras of free Lie algebras and on the Lie algebra associated to the lower central series of a group." Thesis, McGill University, 1987. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=63885.

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22

Yalcinkaya, Sukru. "Black Box Groups And Related Group Theoretic Constructions." Phd thesis, METU, 2007. http://etd.lib.metu.edu.tr/upload/12608546/index.pdf.

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The present thesis aims to develop an analogy between the methods for recognizing a black box group and the classification of the finite simple groups. We propose a uniform approach for recognizing simple groups of Lie type which can be viewed as the computational version of the classification of the finite simple groups. Similar to the inductive argument on centralizers of involutions which plays a crucial role in the classification project, our approach is based on a recursive construction of the centralizers of involutions in black box groups. We present an algorithm which constructs a long root SL_2(q)-subgroup in a finite simple group of Lie type of odd characteristic $p$ extended possibly by a p-group. Following this construction, we take the Aschbacher'
s ``Classical Involution Theorem'
'
as a model in the final recognition algorithm and we propose an algorithm which constructs all root SL_2(q)-subgroups corresponding to the nodes in the extended Dynkin diagram, that is, our approach is the construction of the the extended Curtis - Phan - Tits presentation of the finite simple groups of Lie type of odd characteristic which further yields the construction of all subsystem subgroups which can be read from the extended Dynkin diagram. In this thesis, we present this algorithm for the groups PSL_n(q) and PSU_n(q). We also present an algorithm which determines whether the p-core (or ``unipotent radical'
'
) O_p(G) of a black box group G is trivial or not where G/O_p(G) is a finite simple classical group of Lie type of odd characteristic p answering a well-known question of Babai and Shalev. The algorithms presented in this thesis have been implemented extensively in the computer algebra system GAP.

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Nikolaishvili, George. "Investigation of the Equations Modelling Chemical Waves Using Lie Group Analysis." Thesis, Blekinge Tekniska Högskola, Sektionen för ingenjörsvetenskap, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:bth-3996.

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A system of nonlinear di fferential equations, namely, the Belousov-Zhabotinskii reaction model has been investigated for nonlinear self-adjointness using the recent work of Professor N.H.Ibragimov. It is shown that the model is not nonlinearly self-adjoint. The symmetries of the system and nonlinear conservation laws are calculated. The modi fied system, which is nonlinearly self-adjoint, is also analysed. Its symmetries and conservation laws are presented.

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Aubert, Anne. "Structures affinées et pseudo-métriques invariantes à gauche sur des groupes de Lie." Montpellier 2, 1996. http://www.theses.fr/1996MON20225.

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Le but de ce travail est double. D'une part etudier les groupes de lie affine (i. E. Munis d'une structure affine invariante a gauche) dont la structure affine est liee a une pseudo-metrique invariante a gauche. Nous prouvons en particulier les resultats suivants: la structure affine d'un groupe de lie pseudo-riemannien plat est geodesiquement complete si et seulement si le groupe est unimodulaire. La variete cotangente d'un groupe de lie connexe et simplement connexe est munie d'une structure de groupe de lie pseudo-riemannien plat. D'autre part, introduire une technique dite de double extension, inspiree de celle de medina-revoy, capable de decrire les algebres de lie de certains groupes de lie affines a pseudo-metrique invariante a gauche hessienne. C'est ainsi que nous caracterisons les algebres de lie. Des groupes de lie nilpotents lorentziens plats des groupes de lie pseudo-riemanniens plats ou la connexion de levi-civita est bi-invariante des groupes de lie a structure affine et a pseudo-metrique localement hessienne bi-invariantes des groupes de lie symplectiques a pseudo-metrique bi-invariante

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25

Nishiyama, Kyo. "Representations of Weyl groups and their Hecke algebras on virtual character modules of a semisimple Lie group." 京都大学 (Kyoto University), 1986. http://hdl.handle.net/2433/86366.

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Günther, Janne-Kathrin. "The C*-algebras of certain Lie groups." Thesis, Université de Lorraine, 2016. http://www.theses.fr/2016LORR0118/document.

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Dans la présente thèse de doctorat, les C*-algèbres des groupes de Lie connexes réels nilpotents de pas deux et du groupe de Lie SL(2,R) sont caractérisées. En outre, comme préparation à une analyse de sa C*-algèbre, la topologie du spectre du produit semi-direct U(n) x H_n est décrite, où H_n dénote le groupe de Lie de Heisenberg et U(n) le groupe unitaire qui agit sur H_n par automorphismes. Pour la détermination des C*-algèbres de groupes, la transformation de Fourier à valeurs opérationnelles est utilisée pour appliquer chaque C*-algèbre dans l'algèbre de tous les champs d'opérateurs bornés sur son spectre. On doit trouver les conditions que satisfait l'image de cette C*-algèbre sous la transformation de Fourier et l'objectif est de la caractériser par ces conditions. Dans cette thèse, il est démontré que les C*-algèbres des groupes de Lie connexes réels nilpotents de pas deux et la C*-algèbre de SL(2,R) satisfont les mêmes conditions, des conditions appelées «limites duales sous contrôle normique». De cette manière, ces C*-algèbres sont décrites dans ce travail et les conditions «limites duales sous contrôle normique» sont explicitement calculées dans les deux cas. Les méthodes utilisées pour les groupes de Lie nilpotents de pas deux et pour le groupe SL(2,R) sont très différentes l'une de l'autre. Pour les groupes de Lie nilpotents de pas deux, on regarde leurs orbites coadjointes et on utilise la théorie de Kirillov, alors que pour le groupe SL(2,R), on peut mener les calculs plus directement
In this doctoral thesis, the C*-algebras of the connected real two-step nilpotent Lie groups and the Lie group SL(2,R) are characterized. Furthermore, as a preparation for an analysis of its C*-algebra, the topology of the spectrum of the semidirect product U(n) x H_n is described, where H_n denotes the Heisenberg Lie group and U(n) the unitary group acting by automorphisms on H_n. For the determination of the group C*-algebras, the operator valued Fourier transform is used in order to map the respective C*-algebra into the algebra of all bounded operator fields over its spectrum. One has to find the conditions that are satisfied by the image of this C*-algebra under the Fourier transform and the aim is to characterize it through these conditions. In the present thesis, it is proved that both the C*-algebras of the connected real two-step nilpotent Lie groups and the C*-algebra of SL(2,R) fulfill the same conditions, namely the “norm controlled dual limit” conditions. Thereby, these C*-algebras are described in this work and the “norm controlled dual limit” conditions are explicitly computed in both cases. The methods used for the two-step nilpotent Lie groups and the group SL(2,R) are completely different from each other. For the two-step nilpotent Lie groups, one regards their coadjoint orbits and uses the Kirillov theory, while for the group SL(2,R) one can accomplish the calculations more directly

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27

at, michor@esi ac. "The Generalized Cayley Map from an Algebraic Group to its Lie Algebra." ESI preprints, 2001. ftp://ftp.esi.ac.at/pub/Preprints/esi1066.ps.

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Duff, Ana. "Derivations, invariant forms and the second homology group of orthosymplectic Lie superalgebras." Thesis, University of Ottawa (Canada), 2002. http://hdl.handle.net/10393/6346.

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We develop the description of the derivation algebras of orthosymplectic Lie super-algebras over supercommutative, associative superrings containing ½ and determine conditions under which the derivation algebra can be written as a semidirect product of the inner and the outer derivations. We then describe the supersymmetric invariant forms of the elementary orthosymplectic Lie superalgebra and determine the outer derivations which are skew with respect to a given supersymmetric invariant form. Finally, we describe the universal central extension and its centre, the second homology group, of the elementary orthosymplectic Lie superalgebra. The original motivation for this comes from the theory of extended affine Lie algebras. Specialized to the orthosymplectic Lie superalgebras representing the centreless cores of extended affine Lie algebras of type B and D, the above descriptions are the necessary and sufficient building blocks for the construction of an extended affine Lie algebra of type B and D from its centreless core.

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Sigurdsson, Gunnar. "Canoniical involutions and bosonic representations of three-dimensional lie colour algebras." Licentiate thesis, KTH, Physics, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-1750.

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Lechner, Sabine [Verfasser], and Annette [Akademischer Betreuer] Huber. "A comparison of locally analytic group cohomology and Lie algebra cohomology for p-adic Lie groups = Ein Vergleich lokal analytischer Gruppenkohomologie und Liealgebrenkohomologie für p-adische Liegruppen." Freiburg : Universität, 2011. http://d-nb.info/112346314X/34.

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Günther, Janne-Kathrin. "The C*-algebras of certain Lie groups." Electronic Thesis or Diss., Université de Lorraine, 2016. http://www.theses.fr/2016LORR0118.

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Dans la présente thèse de doctorat, les C*-algèbres des groupes de Lie connexes réels nilpotents de pas deux et du groupe de Lie SL(2,R) sont caractérisées. En outre, comme préparation à une analyse de sa C*-algèbre, la topologie du spectre du produit semi-direct U(n) x H_n est décrite, où H_n dénote le groupe de Lie de Heisenberg et U(n) le groupe unitaire qui agit sur H_n par automorphismes. Pour la détermination des C*-algèbres de groupes, la transformation de Fourier à valeurs opérationnelles est utilisée pour appliquer chaque C*-algèbre dans l'algèbre de tous les champs d'opérateurs bornés sur son spectre. On doit trouver les conditions que satisfait l'image de cette C*-algèbre sous la transformation de Fourier et l'objectif est de la caractériser par ces conditions. Dans cette thèse, il est démontré que les C*-algèbres des groupes de Lie connexes réels nilpotents de pas deux et la C*-algèbre de SL(2,R) satisfont les mêmes conditions, des conditions appelées «limites duales sous contrôle normique». De cette manière, ces C*-algèbres sont décrites dans ce travail et les conditions «limites duales sous contrôle normique» sont explicitement calculées dans les deux cas. Les méthodes utilisées pour les groupes de Lie nilpotents de pas deux et pour le groupe SL(2,R) sont très différentes l'une de l'autre. Pour les groupes de Lie nilpotents de pas deux, on regarde leurs orbites coadjointes et on utilise la théorie de Kirillov, alors que pour le groupe SL(2,R), on peut mener les calculs plus directement
In this doctoral thesis, the C*-algebras of the connected real two-step nilpotent Lie groups and the Lie group SL(2,R) are characterized. Furthermore, as a preparation for an analysis of its C*-algebra, the topology of the spectrum of the semidirect product U(n) x H_n is described, where H_n denotes the Heisenberg Lie group and U(n) the unitary group acting by automorphisms on H_n. For the determination of the group C*-algebras, the operator valued Fourier transform is used in order to map the respective C*-algebra into the algebra of all bounded operator fields over its spectrum. One has to find the conditions that are satisfied by the image of this C*-algebra under the Fourier transform and the aim is to characterize it through these conditions. In the present thesis, it is proved that both the C*-algebras of the connected real two-step nilpotent Lie groups and the C*-algebra of SL(2,R) fulfill the same conditions, namely the “norm controlled dual limit” conditions. Thereby, these C*-algebras are described in this work and the “norm controlled dual limit” conditions are explicitly computed in both cases. The methods used for the two-step nilpotent Lie groups and the group SL(2,R) are completely different from each other. For the two-step nilpotent Lie groups, one regards their coadjoint orbits and uses the Kirillov theory, while for the group SL(2,R) one can accomplish the calculations more directly

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32

To, Kai-ming Simon, and 杜啟明. "On some aspects of a Poisson structure on a complex semisimple Lie group." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2011. http://hub.hku.hk/bib/B45700333.

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Seiler, Konstantin. "Fast trajectory generation and correction for non-holonomic systems exploiting Lie group symmetries." Thesis, The University of Sydney, 2013. http://hdl.handle.net/2123/10117.

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Sampling based motion planning is a popular motion planning technique for systems with many degrees of freedom in continuous state spaces. In particular the class of Rapidly exploring Random Tree algorithms (RRTs) has wide-spread use as they can be applied to a broad range of systems. Subsequently many extensions and variations to the RRT algorithm are known today. Many results, however, are not applicable in the case of non-holonomic and underactuated systems due to the difficulty in obtaining the required length-of-shortest-path distance metric and corresponding local planner. Instead, by focussing on changing existing paths this work develops algorithmic frameworks that allow faster motion planning specifically in the domain of non-holonomic underactuated systems. In order to adapt the paths efficiently, symmetries exhibited by the system are exploited by the algorithms. The particular focus of this work is on continuous symmetry groups that constitute a Lie group and thus allow for fast and powerful transformations of existing trajectories. Two methods are proposed to address this. The first allows path correction of an arbitrary path to reach a given goal. It works by applying small changes to selected small segments of a given trajectory and propagates their effects in a fast way using symmetry operations that avoid costly reintegration along the whole path. The second method allows the RRT algorithm to plan for a whole family of paths simultaneously to achieve greater coverage of the state space. The algorithm identifies those symmetry orbits, or subspaces thereof, that contain valid paths and propagates their states throughout the planning process. Both methods can be employed together and complement each other well.

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Labsir, Samy. "Méthodes statistiques fondées sur les groupes de Lie pour le suivi d'un amas de débris spatiaux." Thesis, Bordeaux, 2020. http://www.theses.fr/2020BORD0294.

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Dans le contexte de la surveillance spatiale, nous nous intéressons à un amas de débris évoluant en orbite autour de la Terre et observé par un capteur radar.Il est alors constaté que l'ensemble des débris se disperse selon une forme bananoïdale due à leur mouvement contraint par les lois de Kepler.Cette répartition est représentative d'échantillons gaussiens concentréssur le groupe de Lie SE(3) et peut être complètement caractérisée par unematrice de covariance inconnue.Nous proposons dans cette thèse une reformulation originale sur groupe de Liedu modèle d'observation de l'amas. Ce dernier est alors modélisé comme une cibleétendue caractérisée par sa forme et et son centroïde. De cette manière, nous reconsidéronsl'estimation de ces derniers comme un problème d'inférence sur variété.La géométrie de l’amas est ainsi intrinsèquement prise en compte. Deux algorithmes sur groupes de Liesont alors proposés afin d'estimer respectivement de manière statique et dynamique les paramètres de l'amas.Dans une première partie du manuscrit, l'enjeu de la surveillance spatiale est souligné et les principales méthodes de pistage de débris sont rappelées.Dans une seconde partie, les fondements des groupes de Lie sontprésentés. La troisième partie est axée sur les contributions de la thèse etpropose un modèle et deux algorithmes d'estimation de la forme et du centroïde d’un amas qui sont ensuite testés sur différents scénarios de simulation.La dernière partie est consacrée à une contribution théorique danslaquelle est mise en place une borne d'erreur d'estimation bayésienne sur groupe de Lie
In the context of space surveillance, we are interested in a cluster of debris evolving in orbit around the Earth and observed by a radar sensor.It is then observed that the debris spreads out taking a bananoid shape due to their movement constrained by Kepler's laws.This distribution is representative of concentrated Gaussian samples on the Lie group SE (3) and can be completely characterized by anunknown covariance matrix.We propose in this thesis an original reformulation of the cluster observation model on Lie groups. The latter is then modeled as an extended targetcharacterized by its shape and its centroid. In this way, we reconsiderits estimation as a manifold inference problem.The geometry of the cluster is thus intrinsically taken into account. Two algorithms on Lie groups are then proposed in order to estimate respectively statically and dynamically the parameters of the cluster.In the first part of the manuscript, the issue of space surveillance is underlined and the main methods for tracking debris are recalled.In a second part, the foundations of Lie groups arepresented. The third part focuses on the contributions of the thesis andproposes a model and two algorithms for estimating the shape and centroid of a cluster which are then tested on different simulation scenarios.The last part is devoted to a theoretical contribution inwhich is proposed a bound for Bayesian estimation error on Lie groups

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35

Volkmann, Jörg. "Exhaust systems' models investigation by theoretical group methods." Göttingen Cuvillier, 2007.

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Birembaux, Olivier. "Actions de groupes résolubles scindement de f-fibres hermitiens." Valenciennes, 1997. https://ged.uphf.fr/nuxeo/site/esupversions/b7bd7233-5e92-4465-8cce-ff9ef4078593.

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Première partie : Soient G un groupe de Lie connexe de dimension n - 1, f une action localement libre de classe Cr (avec r supérieure ou égale à 2) de G sur une variété compacte M de dimension n supérieure ou égale a 3. Nous supposons qu'il existe dans l'algèbre de Lie de G un champ Y tel que la partie réelle de chaque valeur propre de ad(Y) soit strictement plus petite que 0. Alors, nous montrons que f est Cr -conjuguée à une action modèle de G sur un espace homogène H/T ou H est un groupe de Lie contenant G. Nos hypothèses impliquent que G a une structure particulière, mais il existe quand même de nombreux exemples : Notamment, la famille des groupes G ayant cette propriété est continue en toute dimension plus grande que 4 ; pour un choix générique de G, le groupe H correspondant n'a aucun quotient compact de dimension n, et ceci fournit une famille continue de groupes de Lie ne possédant aucune action de codimension 1 suffisamment régulière sur une variété compacte. Ces résultats sont liés à la théorie d'Anosov. Deuxième partie : Soient M une variété C connexe, munie d'un flot F et E un F-fibré hermitien au-dessus de M. On donne une version basique du théorème de Leray-Hirsch pour le fibré P(E), projectifié de E. Ensuite on établit un « principe de scindement » feuilleté, i. E on montre qu'il existe une variété B munie d'un flot V et une application feuilletée σ : B vers M telles que le fibré vectoriel image réciproque σ -1 E se décompose en somme directe de V-fibrés hermitiens Si de rang 1 et l'application σ*, induite en cohomologie basique, est injective.

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37

Miquel, Sebastien. "Arithméticité de sous-groupes discrets contenant un réseau horosphérique." Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLS579/document.

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Soit G un groupe algébrique réel simple de rang réel au moins 2 et P un sous-groupe parabolique de G. On montre que tout sous-groupe discret de G intersectant le radical unipotent de P en un réseau est un réseau aritmétique de G, sauf éventuellement lorsque G = SO(2,4n+2) et P est le stabilisateur d'un 2-plan isotrope. Ceci répond partiellement à une conjecture de Margulis, déjà étudiée par Hee Oh. On étudie aussi le cas où G est le produit de plusieurs groupes de rang 1, généralisant des résultats de Selberg, Benoist et Oh
Let G be a real algebraic group of real rank at least 2 and P a parabolic subgroup of G. We prove that any discrete subgroup of G that intersects the unipotent radical of P in a lattice is an arithmetic lattice of G, except maybe when G=SO(2,4n+2) and P is the stabilizer of an isotropic 2-plane. This provide a partial answer to a conjecture of Margulis that was already studied by Hee Oh. We also study the case where G is a product of several rank 1 groups, generalising results of Selberg, Benoist and Oh

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38

Wiseman, Robin D. "The Jahn-Teller effect in icosahedral symmetry : unexpected lie group symmetries and their exploitation." Thesis, University of Oxford, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.299385.

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Watts, Gerard Marcel Tannerie. "Extended algebras in conformal field theory." Thesis, University of Cambridge, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.277913.

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Roa, Aguirre Alexis [UNESP]. "Fluxo do grupo de renormalização dos modelos-'alfa' e as álgebras de Lie contínuas." Universidade Estadual Paulista (UNESP), 2008. http://hdl.handle.net/11449/138379.

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Made available in DSpace on 2016-05-17T16:51:02Z (GMT). No. of bitstreams: 0 Previous issue date: 2008-08-29. Added 1 bitstream(s) on 2016-05-17T16:54:20Z : No. of bitstreams: 1 000854764.pdf: 562890 bytes, checksum: 164c6db1a3c04e45b5f0eea9ea15e58e (MD5)
Este trabalho é basicamente uma revisão de alguns aspectos de integrabilidade em duas dimensões discutidos no artigo Renormalization group ﬂows and continual Lie algebras do professor Ioannis Bakas. A idéia é estudar o ﬂuxo do grupo de renormalização das métricas bi-dimensionais nos modelos-'alfa' usando a função beta a 1-loop, e mostrar que elas fornecem análogos contínuos das equações de campo de Toda nas coordenadas conformemente planas do espaço target. Nesta formulção algébrica, a escala logaritmica de comprimento da folha mundo é interpretada como o parâmetro de Dynkin num sistema de raízes de uma álgebra de Lie contínua, denotada por G(d/dt;II), com um kernel de Cartan generalizado anti-simétrico K(t,t') = 'alfa'(t−t'). Usando o formalismo de curvatura zero construiremos a solução geral do ﬂuxo do grupo de renormalização em termos das conﬁgurações de campo livre por meio de transformações de Bäcklund. A validade desta solução geral como uma expansão em serie de potência será testada com alguns exemplos especiais que incluim o modelo sausage, as métricas de curvatura constante negativa e a queda de singularidades côonicas
This work is basically a review of some aspect of the integrability in two dimensions discussed in the Prof. Ioannis Bakas's paper called Renormalization group ﬂows and continual Lie algebras. The main idea is to study the renormalization group ﬂow of two-dimensional metrics in sigma models using the one-loop beta function, and demonstrate that they provide a continual analogue of the Toda ﬁeld equations in conformally ﬂat coordinates in the target space. In this algebraic frame, the logarithm of the world-sheet length scale t is interpreted as Dynkin parameter on the root system of a continual Lie algebra, denoted by G(d/dt;II),witha an ti-symmetric generalized Cartan kernel K(t,t') ='sigmma'(t−t'). Using the zero curvature formalism, we construct a general solution of the renormalization group ﬂow in terms of the free ﬁeld conﬁgurations via B¨acklund transformations. The validity of these general solutions as a power series expansion is veriﬁed in some specials examples including the sausage model, the constant negative curvature metrics and the decay of conical singularities

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41

Roa, Aguirre Alexis. "Fluxo do grupo de renormalização dos modelos-'alfa' e as álgebras de Lie contínuas /." São Paulo, 2008. http://hdl.handle.net/11449/138379.

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Orientador: Abraham Hirsz Zimerman
Banca: Nathan Jacob Berkovits
Banca: Victor de Oliveira Rivelles
Resumo: Este trabalho é basicamente uma revisão de alguns aspectos de integrabilidade em duas dimensões discutidos no artigo "Renormalization group ﬂows and continual Lie algebras" do professor Ioannis Bakas. A idéia é estudar o ﬂuxo do grupo de renormalização das métricas bi-dimensionais nos modelos-'alfa' usando a função beta a 1-loop, e mostrar que elas fornecem análogos contínuos das equações de campo de Toda nas coordenadas conformemente planas do espaço target. Nesta formulção algébrica, a escala logaritmica de comprimento da folha mundo é interpretada como o parâmetro de Dynkin num sistema de raízes de uma álgebra de Lie contínua, denotada por G(d/dt;II), com um kernel de Cartan generalizado anti-simétrico K(t,t') = 'alfa'(t−t'). Usando o formalismo de curvatura zero construiremos a solução geral do ﬂuxo do grupo de renormalização em termos das conﬁgurações de campo livre por meio de transformações de Bäcklund. A validade desta solução geral como uma expansão em serie de potência será testada com alguns exemplos especiais que incluim o modelo "sausage", as métricas de curvatura constante negativa e a queda de singularidades côonicas
Abstract: This work is basically a review of some aspect of the integrability in two dimensions discussed in the Prof. Ioannis Bakas's paper called "Renormalization group ﬂows and continual Lie algebras". The main idea is to study the renormalization group ﬂow of two-dimensional metrics in sigma models using the one-loop beta function, and demonstrate that they provide a continual analogue of the Toda ﬁeld equations in conformally ﬂat coordinates in the target space. In this algebraic frame, the logarithm of the world-sheet length scale t is interpreted as Dynkin parameter on the root system of a continual Lie algebra, denoted by G(d/dt;II),witha an ti-symmetric generalized Cartan kernel K(t,t') ='sigmma'(t−t'). Using the zero curvature formalism, we construct a general solution of the renormalization group ﬂow in terms of the free ﬁeld conﬁgurations via B¨acklund transformations. The validity of these general solutions as a power series expansion is veriﬁed in some specials examples including the sausage model, the constant negative curvature metrics and the decay of conical singularities
Mestre

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42

Manjarín, Arcas Mònica. "Study of a class of compact complex manifolds." Doctoral thesis, Universitat Autònoma de Barcelona, 2006. http://hdl.handle.net/10803/3092.

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43

丸橋, 広和. "単連結べき零Lie群のパラメータ剛性をもつ作用." 京都大学 (Kyoto University), 2014. http://hdl.handle.net/2433/188455.

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Valencia, Jorge J. "Lie theory for some quotients of the affine group represented by the Hopf Shuffle algebra." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape15/PQDD_0004/NQ34850.pdf.

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45

Bright, Theresa Ann. "New solutions to the euler equations using lie group analysis and high order numerical techniques." Diss., Georgia Institute of Technology, 1993. http://hdl.handle.net/1853/29990.

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46

Uemura, Hideaki. "Off-Diagonal Short Time Expansion of the Heat Kernel on a Certain Nilpotent Lie Group." 京都大学 (Kyoto University), 1989. http://hdl.handle.net/2433/86399.

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Faccin, Paolo. "Computational problems in algebra: units in group rings and subalgebras of real simple Lie algebras." Doctoral thesis, Università degli studi di Trento, 2014. https://hdl.handle.net/11572/368142.

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In the first part of the thesis I produce and implement an algorithm for obtaining generators of the unit group of the integral group ring ZG of finite abelian group G. We use our implementation in MAGMA of this algorithm to compute the unit group of ZG for G of order up to 110. In the second part of the thesis I show how to construct multiplication tables of the semisimple real Lie algebras. Next I give an algorithm, based on the work of Sugiura, to find all Cartan subalgebra of such a Lie algebra. Finally I show algorithms for finding semisimple subalgebras of a given semisimple real Lie algebra.

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Faccin, Paolo. "Computational problems in algebra: units in group rings and subalgebras of real simple Lie algebras." Doctoral thesis, University of Trento, 2014. http://eprints-phd.biblio.unitn.it/1182/1/PhdThesisFaccinPaolo.pdf.

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In the first part of the thesis I produce and implement an algorithm for obtaining generators of the unit group of the integral group ring ZG of finite abelian group G. We use our implementation in MAGMA of this algorithm to compute the unit group of ZG for G of order up to 110. In the second part of the thesis I show how to construct multiplication tables of the semisimple real Lie algebras. Next I give an algorithm, based on the work of Sugiura, to find all Cartan subalgebra of such a Lie algebra. Finally I show algorithms for finding semisimple subalgebras of a given semisimple real Lie algebra.

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Lee, Hyereem, and Hyereem Lee. "Triples in Finite Groups and a Conjecture of Guralnick and Tiep." Diss., The University of Arizona, 2017. http://hdl.handle.net/10150/624584.

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In this thesis, we will see a way to use representation theory and the theory of linear algebraic groups to characterize certain family of finite groups. In Chapter 1, we see the history of preceding work. In particular, J. G. Thompson’s classification of minimal finite simple nonsolvable groups and characterization of solvable groups will be given. In Chapter 2, we will describe some background knowledge underlying this project and notation that will be widely used in this thesis. In Chapter 3, the main theorem originally conjectured by Guralnick and Tiep will be stated together with the base theorem which is a reduced version of main theorem to the case where we have a quasisimple group. Main theorem explains a way to characterize the finite groups with a composition factor of order divisible by two distinct primes p and q as the finite groups containing nontrivial 2-element x, p-element y, q-element z such that xyz = 1. In this thesis we more focus on the proof of showing a finite group G with a composition factor of order divisible by two distinct prime p and q contains nontrivial 2-element x, p-element y, q-element z such that xyz = 1. In Chapter 4, we will prove a set of lemmas and proposition which will be used as key tools in the proof of the base theorem. In Chapters 5 to 7, we will establish the base theorem in the cases where a quasisimple group G has its simple quotient isomorphic to alternating groups or sporadic groups (Chapter 5), classical groups (Chapter 6), and exceptional groups (Chapter 7). In Chapter 8, we show that any finite group G admitting nontrivial 2-element x, p- element y, q-element z such that xyz = 1 for two distinct odd primes p and q admits a composition factor of order divisible by pq. Also, we show that the question if a finite group G with a composition factor of order divisible by two distinct prime p and q contains nontrivial 2-element x, p-element y, q-element z such that xyz = 1 can be reduced to the base theorem.

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Caprace, Pierre-Emmanuel. ""Abstract" homomorphisms of split Kac-Moody groups." Doctoral thesis, Universite Libre de Bruxelles, 2005. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210962.

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Cette thèse est consacrée à une classe de groupes, appelés groupes de Kac-Moody, qui généralise de façon naturelle les groupes de Lie semi-simples, ou plus précisément, les groupes algébriques réductifs, dans un contexte infini-dimensionnel. On s'intéresse plus particulièrement au problème d'isomorphismes pour ces groupes, en vue d'obtenir un analogue infini-dimensionnel de la célèbre théorie des homomorphismes 'abstraits' de groupes algébriques simples, due à Armand Borel et Jacques Tits.

Le problème d'isomorphismes qu'on étudie s'avère être un cas particulier d'un problème plus général, qui consiste à caractériser les homomorphismes de groupes algébriques vers les groupes de Kac-Moody, dont l'image est bornée. Ce problème peut à son tour s'énoncer comme un problème de rigidité pour les actions de groupes algébriques sur les immeubles, via l'action naturelle d'un groupe de Kac-Moody sur une paire d'immeubles jumelés. Les résultats partiels, relatifs à ce problème de rigidité, que nous obtenons, nous permettent d'apporter une solution complète au problème d'isomorphismes pour les groupes de Kac-Moody déployés.

En particulier, on obtient un résultat de dévissage pour les automorphismes de ces objets. Celui-ci fournit à son tour une description complète de la structure du groupe d'automorphismes d'un groupe de Kac-Moody déployé sur un corps de caractéristique~$0$.

Nos arguments permettent également de traiter de façon analogue certaines formes anisotropes de groupes de Kac-Moody complexes, appelées formes unitaires. On montre en particulier que la topologie Hausdorff naturelle que portent ces formes est un invariant de leur structure de groupe abstrait. Ceci généralise un résultat bien connu de H. Freudenthal pour les groupes de Lie compacts.

Enfin, l'on s'intéresse aux homomorphismes de groupes de Kac-Moody à image fini-dimensionnelle, et l'on démontre la non-existence de tels homomorphismes à noyau central, lorsque le domaine est un groupe de Kac-Moody de type indéfini sur un corps infini. Ceci réduit un problème ouvert, dit problème de linéarité pour les groupes de Kac-Moody, au cas de corps de base finis.
Doctorat en sciences, Spécialisation mathématiques
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Dissertations / Theses on the topic 'Lie group'

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