Cocharacters of group graded algebras and multiplicities bounded by one

Abstract

Let G be a finite group and A a G-graded algebra over a field F of characteristic zero. We characterize the -ideals of graded identities of A such that the multiplicities in the graded cocharacter of A are bounded by one. We do so by exhibiting a set of identities of the -ideal. As a consequence we characterize the varieties of G-graded algebras whose lattice of subvarieties is distributive.