On the *-polynomial identities of M_{1;1}(E)

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).