Graded A-identities for the matrix algebra of order two

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)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.Let F be a field of characteristic 0 and let R = M2(F). The algebra R admits a natural grading R = R0 ⊕ R1 by the cyclic group Z2 of order 2. In this paper, we describe the Z2-graded A-identities for R. Recall that an A-identity for an algebra is a multil26816171631FAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)2014/09310-5480139/2012-1; 304632/2015-