G-identities for the Lie algebra sl(2)(C)

Autor(es)

Koshlukov, Plamen ^[1] ; Mattos Mortari, Alda Dayana ^[1]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, IMECC, Dept Math, BR-18083859 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Pure and Applied Algebra; v. 219, n. 6, p. 2381-2395, JUN 2015.
• Citações Web of Science: 0

Resumo

In this paper we study the G-identities for the Lie algebra sl(2)(C) over the complex field C. If sl(2)(C) is acted on faithfully by a finite group G then G is isomorphic to one of the following groups: C-n, D-n, A(4), S-4, A(5). Here C-n is the cyclic group of order n, D-n is the dihedral group (of order 2n), A(n) and S-n stand for the alternating and for the symmetric group permuting n letters, respectively. In each one of the above cases we describe a basis of the G-identities for sl(2)(C). In order to do that we use the explicit form of the graded identities for sl(2)(C) as well as properties of the group algebras of the corresponding groups. The same problem for the associative algebra M-2(C) of the 2 x 2 matrices was settled by A. Berele in 2004. (C) 2014 Elsevier B.V. All rights reserved. (AU)

• Processo FAPESP: 10/50347-9 - Álgebras, representações e aplicações
• Beneficiário: Ivan Chestakov
• Modalidade de apoio: Auxílio à Pesquisa - Temático