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Relevant bibliographies by topics / Maximal Subalgebra

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Academic literature on the topic 'Maximal Subalgebra'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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Journal articles on the topic "Maximal Subalgebra"

1

Laliena, Jesús. "The Frattini subalgebra of a Bernstein algebra." Proceedings of the Edinburgh Mathematical Society 35, no. 3 (1992): 397–403. http://dx.doi.org/10.1017/s001309150000568x.

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Let A be a finite-dimensional Bernstein algebra over a field K with characteristic not 2. Maximal subalgebras of A are studied, and they are determined if A is a genetic algebra. It is also proved that the intersection of all maximal subalgebras of A (the Frattini subalgebra of A) is always an ideal. Finally the structure of Bernstein algebras with Frattini subalgebra equal to zero is described.

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Towers, David A. "The index complex of a maximal subalgebra of a Lie algebra." Proceedings of the Edinburgh Mathematical Society 54, no. 2 (2011): 531–42. http://dx.doi.org/10.1017/s0013091509001035.

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AbstractLet M be a maximal subalgebra of the Lie algebra L. A subalgebra C of L is said to be a completion for M if C is not contained in M but every proper subalgebra of C that is an ideal of L is contained in M. The set I(M) of all completions of M is called the index complex of M in L. We use this concept to investigate the influence of the maximal subalgebras on the structure of a Lie algebra, in particular, finding new characterizations of solvable and supersolvable Lie algebras.

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Conti, Roberto, Jeong Hee Hong, and Wojciech Szymański. "On conjugacy of maximal abelian subalgebras and the outer automorphism group of the Cuntz algebra." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 145, no. 2 (2015): 269–79. http://dx.doi.org/10.1017/s0308210513001364.

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We investigate the structure of the outer automorphism group of the Cuntz algebra and the closely related problem of conjugacy of maximal abelian subalgebras in . In particular, we exhibit an uncountable family of maximal abelian subalgebras, conjugate to the standard maximal abelian subalgebra via Bogolubov automorphisms, that are not inner conjugate to .

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Adams, M. E. "Maximal subalgebras of Heyting algebras." Proceedings of the Edinburgh Mathematical Society 29, no. 3 (1986): 359–65. http://dx.doi.org/10.1017/s0013091500017806.

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AHeyting algebra is an algebra H;∨,∧ →, 0,1) of type (2,2,2,0,0) for which H;∨,∧,0,1) is a bounded distributive lattice and → is the binary operation of relative pseudocomplementation (i.e., for a,b,c∈H,ac ∧≦birr c≦a→b). Associated with every subalgebra of a Heyting algebra is a separating set. Those corresponding to maximal subalgebras are characterized in Proposition 8 and, subsequently, are used in an investigation of Heyting algebras.

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RAJARAMA BHAT, B. V., FRANCO FAGNOLA, and MICHAEL SKEIDE. "MAXIMAL COMMUTATIVE SUBALGEBRAS INVARIANT FOR CP-MAPS: (COUNTER-)EXAMPLES." Infinite Dimensional Analysis, Quantum Probability and Related Topics 11, no. 04 (2008): 523–39. http://dx.doi.org/10.1142/s0219025708003269.

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We solve, mainly by counterexamples, many natural questions regarding maximal commutative subalgebras invariant under CP-maps or semigroups of CP-maps on a von Neumann algebra. In particular, we discuss the structure of the generators of norm continuous semigroups on [Formula: see text] leaving a maximal commutative subalgebra invariant and show that there exist Markov CP-semigroups on Md without invariant maximal commutative subalgebras for any d > 2.

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Neeb, Karl-Hermann, and Ivan Penkov. "Cartan Subalgebras of." Canadian Mathematical Bulletin 46, no. 4 (2003): 597–616. http://dx.doi.org/10.4153/cmb-2003-056-1.

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AbstractLet V be a vector space over a field of characteristic zero and V* be a space of linear functionals on V which separate the points of V. We consider V ⊗ V* as a Lie algebra of finite rank operators on V, and set (V, V*) := V ⊗ V*. We define a Cartan subalgebra of (V, V*) as the centralizer of a maximal subalgebra every element of which is semisimple, and then give the following description of all Cartan subalgebras of (V;V*) under the assumption that is algebraically closed. A subalgebra of (V, V*) is a Cartan subalgebra if and only if it equals for some one-dimensional subspaces Vj ⊆

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Bovdi, Victor A., and Ho-Hon Leung. "Maximal commutative subalgebras of a Grassmann algebra." Journal of Algebra and Its Applications 18, no. 07 (2019): 1950139. http://dx.doi.org/10.1142/s0219498819501391.

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We provide a new approach to the investigation of maximal commutative subalgebras (with respect to inclusion) of Grassmann algebras. We show that finding a maximal commutative subalgebra in Grassmann algebras is equivalent to constructing an intersecting family of subsets of various odd sizes in [Formula: see text] which satisfies certain combinatorial conditions. Then we find new maximal commutative subalgebras in the Grassmann algebra of odd rank [Formula: see text] by constructing such combinatorial systems for odd [Formula: see text]. These constructions provide counterexamples to conjectu

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Varea, V. R. "Lower semimodular Lie algebras." Proceedings of the Edinburgh Mathematical Society 42, no. 3 (1999): 521–40. http://dx.doi.org/10.1017/s0013091500020496.

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This paper is concerned with the relationship between the properties of the subalgebra lattice ℒ(L) of a Lie algebra L and the structure of L. If the lattice ℒ(L) is lower semimodular, then the Lie algebra L is said to be lower semimodular. If a subalgebra S of L is a modular element in the lattice ℒ(L), then S is called a modular subalgebra of L. The easiest condition to ensure that L is lower semimodular is that dim A/B = 1 whenever B < A ≤ L and B is maximal in A (Lie algebras satisfying this condition are called sχ-algebras). Our aim is to characterize lower semimodular Lie algebras and

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SALEMKAR, ALI REZA, SARA CHEHRAZI, and SOMAIEH ALIZADEH NIRI. "ON THETA PAIRS FOR A MAXIMAL SUBALGEBRA." Journal of Algebra and Its Applications 11, no. 01 (2012): 1250001. http://dx.doi.org/10.1142/s0219498811005257.

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Given a maximal subalgebra M of a finite-dimensional Lie algebra L, a θ-pair for M is a pair (A, B) of subalgebras such that A ≰ M, B is an ideal of L contained in A ∩ M, and A/B includes properly no nonzero ideal of L/B. This is analogous to the concept of θ-pairs associated to maximal subgroups of a finite group, which has been studied by a number of authors. A θ-pair (A, B) for M is said to be maximal if M has no θ-pair (C, D) such that A < C. In this paper, we obtain some properties of maximal θ-pairs and use them to give some characterizations of solvable, supersolvable and nilpotent L

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Mészáros, Szabolcs. "Cocommutative elements form a maximal commutative subalgebra in quantum matrices." Journal of Algebra and Its Applications 17, no. 09 (2018): 1850179. http://dx.doi.org/10.1142/s0219498818501797.

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In this paper, we prove that the subalgebras of cocommutative elements in the quantized coordinate rings of [Formula: see text], [Formula: see text] and [Formula: see text] are the centralizers of the trace [Formula: see text] in each algebra, for [Formula: see text] being not a root of unity. In particular, it is not only a commutative subalgebra as it was known before, but it is a maximal one.

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Dissertations / Theses on the topic "Maximal Subalgebra"

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Sistko, Alexander Harris. "Maximal subalgebras of finite-dimensional algebras: with connections to representation theory and geometry." Diss., University of Iowa, 2019. https://ir.uiowa.edu/etd/6857.

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Let $k$ be a field and $B$ a finite-dimensional, associative, unital $k$-algebra. For each $1 \le d \le \dim_kB$, let $\operatorname{AlgGr}_d(B)$ denote the projective variety of $d$-dimensional subalgebras of $B$, and let $\operatorname{Aut}_k(B)$ denote the automorphism group of $B$. In this thesis, we are primarily concerned with understanding the relationship between $\operatorname{AlgGr}_d(B)$, the representation theory of $B$, and the representation theory of $\operatorname{Aut}_k(B)$. We begin by proving fundamental structure theorems for the maximal subalgebras of $B$. We show that max

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Gontcharov, Aleksandr. "On the Conjugacy of Maximal Toral Subalgebras of Certain Infinite-Dimensional Lie Algebras." Thèse, Université d'Ottawa / University of Ottawa, 2013. http://hdl.handle.net/10393/26086.

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We will extend the conjugacy problem of maximal toral subalgebras for Lie algebras of the form $\g{g} \otimes_k R$ by considering $R=k[t,t^{-1}]$ and $R=k[t,t^{-1},(t-1)^{-1}]$, where $k$ is an algebraically closed field of characteristic zero and $\g{g}$ is a direct limit Lie algebra. In the process, we study properties of infinite matrices with entries in a B\'zout domain and we also look at how our conjugacy results extend to universal central extensions of the suitable direct limit Lie algebras.

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Purslow, Thomas. "Maximal subalgebras of the exceptional Lie algebras in low characteristic." Thesis, University of Manchester, 2018. https://www.research.manchester.ac.uk/portal/en/theses/maximal-subalgebras-of-the-exceptional-lie-algebras-in-low-characteristic(8ebc7b9a-98fe-4ab0-82a9-ab71ef89fdb9).html.

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Thomova, Zora. "Maximal abelian subalgebras of pseudoeuclidean real Lie algebras and their application in physics." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape11/PQDD_0023/NQ38840.pdf.

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Scharfenberger-Fabian, Gido [Verfasser]. "Subalgebras of small Souslin Algebras and maximal chains in Souslin Algebras / Gido Scharfenberger-Fabian." Berlin : Freie Universität Berlin, 2008. http://d-nb.info/1023258641/34.

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Junior, Fernando Martins Antoneli. "Subalgebras maximais das álgebras de Lie semisimples, quebra de simetria e o código genético." Universidade de São Paulo, 1998. http://www.teses.usp.br/teses/disponiveis/45/45132/tde-01092009-171526/.

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O propósito deste trabalho é dar uma contribuição ao projeto iniciado por Hornos & Hornos que visa explicar as degenerescências do código genético como resultado de sucessivas quebras de simetria ocorridas durante sua evolução. O modelo matemático usado requer a construção de todas as representações irredutíveis de dimensão 64 das álgebras de Lie simples (chamadas representações de códons) e a análise de suas regras de ramicação sob redução a subalgebras. A classicação de todas as possibilidades é baseada na classicação das subalgebras maximais das álgebras de Lie semisimples obtida por Dynkin

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Boutonnet, Rémi. "Plusieurs aspects de rigidité des algèbres de von Neumann." Thesis, Lyon, École normale supérieure, 2014. http://www.theses.fr/2014ENSL0901/document.

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Dans cette thèse je m'intéresse à des propriétés de rigidité de certaines constructions d'algèbres de von Neumann. Ces constructions relient la théorie des groupes et la théorie ergodique au monde des algèbres d'opérateurs. Il est donc naturel de s'interroger sur la force de ce lien et sur la possibilité d'un enrichissement mutuel dans ces différents domaines. Le Chapitre II traite des actions Gaussiennes. Ce sont des actions de groupes discrets préservant une mesure de probabilité qui généralisent les actions de Bernoulli. Dans un premier temps, j'étudie les propriétés d'ergodicité de ces act

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Larouche, Michelle. "Brisure de symétrie par la réduction des groupes de Lie simples à leurs sous-groupes de Lie réductifs maximaux." Thèse, 2012. http://hdl.handle.net/1866/9105.

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Dans ce travail, nous exploitons des propriétés déjà connues pour les systèmes de poids des représentations afin de les définir pour les orbites des groupes de Weyl des algèbres de Lie simples, traitées individuellement, et nous étendons certaines de ces propriétés aux orbites des groupes de Coxeter non cristallographiques. D'abord, nous considérons les points d'une orbite d'un groupe de Coxeter fini G comme les sommets d'un polytope (G-polytope) centré à l'origine d'un espace euclidien réel à n dimensions. Nous introduisons les produits et les puissances symétrisées de G-polytopes et nous en

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Books on the topic "Maximal Subalgebra"

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Witernitz, P. Maximal Abellian Subalgebras of the Classical Algebras and Their Physical Applications. John Wiley & Sons Inc, 2005.

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Book chapters on the topic "Maximal Subalgebra"

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Stevens, Marco. "Maximal Abelian C $$^*$$ ∗ -Subalgebras." In The Kadison-Singer Property. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-47702-2_4.

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Shchepochkina, Irina. "Maximal Subalgebras of the Classical Linear Lie Superalgebras." In The Orbit Method in Geometry and Physics. Birkhäuser Boston, 2003. http://dx.doi.org/10.1007/978-1-4612-0029-1_18.

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Michel, Louis, and Pavel Winternitz. "Families of transitive primitive maximal simple Lie subalgebras of 𝑑𝑖𝑓𝑓_{𝑛}." In CRM Proceedings and Lecture Notes. American Mathematical Society, 1997. http://dx.doi.org/10.1090/crmp/011/24.

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Pevtsova, Julia, and Jim Stark. "Varieties of Elementary Subalgebras of Maximal Dimension for Modular Lie Algebras." In Geometric and Topological Aspects of the Representation Theory of Finite Groups. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-94033-5_14.

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Kubo, Toshihisa. "On Reducibility Criterions for Scalar Generalized Verma Modules Associated to Maximal Parabolic Subalgebras." In Springer Proceedings in Mathematics & Statistics. Springer Singapore, 2016. http://dx.doi.org/10.1007/978-981-10-2636-2_34.

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"Weights of Irreducible Representations — Maximal Subalgebras." In Group and Representation Theory. WORLD SCIENTIFIC, 2016. http://dx.doi.org/10.1142/9789813202450_0007.

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Brown, William C. "Constructing Maximal Commutative Subalgebras of Matrix Rings." In Rings, extensions, and cohomology. CRC Press, 2020. http://dx.doi.org/10.1201/9781003071815-5.

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Mitra, Debasis, and Florent Launay. "Explanation Generation over Temporal Interval Algebra." In Advances in Geospatial Technologies. IGI Global, 2012. http://dx.doi.org/10.4018/978-1-61692-868-1.ch008.

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Temporal interval algebra has generated strong interest for both theoretical and practical reasons. All its Maximal Tractable Subalgebras (MTS) have been identified. Now is the time to make the transition toward their practical applications. In this chapter, the authors have proposed a formalism on how to classify an input temporal network in one of these MTSs or decide its intractability. They have also proposed a linear algorithm for checking consistency when the input belongs to one of the seventeen MTSs, and for finding the constraints responsible for inconsistency in case the network is unsatisfiable.

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Conference papers on the topic "Maximal Subalgebra"

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Fagnola, Franco, and Michael Skeide. "Restrictions of CP-semigroups to maximal commutative subalgebras." In Noncommutative Harmonic Analysis with Applications to Probability. Institute of Mathematics Polish Academy of Sciences, 2007. http://dx.doi.org/10.4064/bc78-0-8.

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