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Type: Artigo
Title: Elementary Gradings On The Lie Algebra Utn(-)
Author: Koshlukov
Plamen; Yukihide
Abstract: The algebras UTn(K) of the 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. In this paper we consider the Lie algebra UTn(K)((-)) of all upper triangular matrices of order n. We study the group gradings on this algebra. It turns out that the gradings on the Lie algebra UTn(K) are much more intricate than those in the associative case. In this paper we describe the elementary gradings on the Lie algebra UTn(K)((-)). Finally we study the canonical grading on UTn(K)((-)) by the cyclic group Z(n) of order n. We produce a (finite) basis of the graded polynomial identities satisfied by this grading. (C) 2016 Elsevier Inc. All rights reserved.
Subject: Graded Polynomial Identities
Upper Triangular Matrices
Graded Lie Algebras
Editor: Academic Press Inc Elsevier Science
San Diego
Rights: fechado
Identifier DOI: 10.1016/j.jalgebra.2016.10.028
Date Issue: 2017
Appears in Collections:Unicamp - Artigos e Outros Documentos

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