On the [formula omitted]-polynomial identities of [formula omitted

Abstract

In this paper we consider the algebra M 1 , 1 ( E ) endowed with the involution ∗ induced by the transposition superinvolution of the superalgebra M 1 , 1 ( F ) of 2 × 2 -matrices over the field F . We study the ∗ -polynomial identities for this algebra in the case of characteristic zero. We describe a finite set generating the ideal of its ∗ -identities. We also consider M n ( E ) , the algebra of n × n matrices over the Grassmann algebra E . We prove that for a large class of involutions defined on it any ∗ -polynomial identity is indeed a polynomial identity. A similar result holds for the verbally prime algebra M k , l ( E ) .