Polynomial identities in matrix algebras with pseudoinvolution

Let F be an algebraically closed field of characteristic zero. In this paper we deal with matrix superalgebras (i.e. algebras graded by Z2, the cyclic group of order 2) endowed with a pseudoinvolution. The first goal is to present the classification of the pseudoinvolutions that it is possible to define, up to equivalence, in the full matrix algebra Mn(F) of n × n matrices and on its subalgebra UTn(F) of upper-triangular matrices. Along the way we shall give the generators of the T -ideal of identities for the algebras M2(F), UT2(F) and UT3(F), endowed with all possible inequivalent pseudoinvolutions.