Artículos de revistas
Elementary Gradings On The Lie Algebra Utn(-)
Registro en:
Journal Of Algebra. Academic Press Inc Elsevier Science, v. 473, p. 66 - 79, 2017.
0021-8693
1090-266X
WOS:000392675400003
10.1016/j.jalgebra.2016.10.028
Autor
Koshlukov
Plamen; Yukihide
Felipe
Institución
Resumen
Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) 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. 473 66 79 FAPESP [2014/09310-5] CNPq [304632/2015-5] Sao Paulo Research Foundation (FAPESP) [2013/22802-1] Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)