Artem Lopatin
Omsk Branch of Sobolev Institute of Mathematics, SBRAS, Russia
Matrix identities with forms.
April 11, 2012
Abstract: We start with the notion of polynomial identity and recall the classical results on identities of 2x2 matrices over a field of zero characteristic. It is well-known that the problem of description of all identities of the algebra of n x n matrices over an arbitrary field is "hard". In characteristic zero case Razmyslov in 1974 and Procesi in 1976 considered the algebra of n x n matrices together with traces of products of matrices and described its T-ideal of identities. In the case of arbitrary characteristic it is necessary to consider all coefficients of the characteristic polynomial of an n x n matrix instead of the trace. The resulting algebra is called the algebra of n x n matrices with forms. In 1996 Zubkov applied results of Donkin to establish an infinite set of identities that generate the T-ideal K of identities of the algebra of n x n matrices with forms. In this talk we present the finite generating set of the T-ideal K. In particular, K is finitely based.