Gradings and graded linear maps on algebras

Abstract

Let A be a superalgebra over a field F of characteristic zero. We prove tight relations between graded automorphisms, pseudoautomorphisms, superautomorphisms and K-gradings on A, where K is the Klein group. Moreover, we investigate the consequences of such connections within the theory of polynomial identities. In the second part we focus on the superalgebra UTn(F) of n x n upper triangular matrices by completely classifying the graded-pseudo-super automorphism that one can define on it. Finally, we compute the ideals of identities of UTn(F) endowed with a graded or a pseudo automorphism, for any n, and the ideals of identities with super-automorphism in the cases n = 2 and n = 3.