Graded A-identities for the matrix algebra of order two

Autor(es)

Brandao, Jr., Antonio Pereira ; Goncalves, Dimas Jose ; Koshlukov, Plamen

• Tipo de documento: Artigo Científico
• Fonte: INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION; v. 26, n. 8, p. 1617-1631, DEC 2016.
• Citações Web of Science: 0

Resumo

Let F be a field of characteristic 0 and let R = M-2(F). The algebra R admits a natural grading R = R-0 circle plus R-1 by the cyclic group Z(2) of order 2. In this paper, we describe the Z(2)-graded A-identities for R. Recall that an A-identity for an algebra is a multilinear polynomial identity for that algebra which is a linear combination of the monomials x(sigma)(1) . . . x(sigma)(n) where sigma runs over all even permutations of [1,..., n] that is sigma is an element of A(n), the nth alternating group. We first introduce the notion of an A-identity in the case of graded polynomials, then we describe the graded A-identities for R, and finally we compute the corresponding graded A-codimensions. (AU)

• Processo FAPESP: 14/09310-5 - Estruturas algébricas e suas representações
• Beneficiário: Vyacheslav Futorny
• Modalidade de apoio: Auxílio à Pesquisa - Temático