Please use this identifier to cite or link to this item: http://repositorio.unicamp.br/jspui/handle/REPOSIP/326017
Type: Artigo
Title: Group Gradings On The Lie Algebra Of Upper Triangular Matrices
Group gradings on the Lie algebra of upper triangular matrices
Author: Koshlukov, Plamen
Yukihide, Felipe
Abstract: The algebras UTn, of the n x n upper triangular matrices over a field K are of significant importance in the theory of algebras with polynomial identities. Group gradings on algebras appear in various areas and provide an indispensable tool in the study of the algebraic and combinatorial properties of the algebras in question. We classify the group gradings on the Lie algebra UTn(-).It was proved by Valenti and Zaicev in 2007 that every group grading on the associative algebra UT,, is isomorphic to an elementary grading. The elementary gradings on UTn(-) are also well understood, see [6]. It follows from our results that there are nonelementary gradings on UTn(-)). Thus the gradings on the Lie algebra UT4) are much more intricate than those in the associative case. (C) 2017 Elsevier Inc. All rights reserved.
The algebras UTn, of the n x n upper triangular matrices over a field K are of significant importance in the theory of algebras with polynomial identities. Group gradings on algebras appear in various areas and provide an indispensable tool in the study o
Subject: Gradings On Lie Algebras
Upper Triangular Matrices
Elementary Gradings
Group Graded Algebras
Lie, Álgebra de
Álgebras graduadas
Identidades polinomiais graduadas
Matrizes triangulares superiores
Country: Estados Unidos
Editor: Elsevier
Citation: Journal Of Algebra. Academic Press Inc Elsevier Science, v. 477, p. 294 - 311, 2017.
Rights: fechado
fechado
Identifier DOI: 10.1016/j.jalgebra.2016.12.033
Address: https://www.sciencedirect.com/science/article/pii/S0021869317300303
Date Issue: 2017
Appears in Collections:IMECC - Artigos e Outros Documentos

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