Weak polynomial identities for the matrix algebras

Abstract

We study the weak polynomial identities for the matrix algebras over a field K of characteristic 0, i.e.the polynomials from the free associative algebra which vanish on the Lie subalgebra sl k of thek×k matrix algebra M k.There are two main results in the paper, (i) We describe all weak identities which are of degree K–1 in the yi’s.(ii) We find all the weak identities of degree 6 for M 3.One of them gives rise to the central polynomial of degree 8 for M 3 discovered by one of the authors and Azniv Kasparian.