Central polynomials for low order matrix algebras with involution1

Abstract

In the paper we investigate central polynomials for the matrix algebra with symplectic involution *. Their form is inspired by an approach of Formanek and Bergman for investigating matrix identities by means of commutative algebra. We find a necessary condition for the existence of central polynomials of the considered type and define their minimal degree. A description of such central polynomials for M 4(K.*) is given. Some investigations are made for M 6(K.*).