Graded polynomial identities of triangular algebras

Abstract

Let F be any field, G a finite abelian group and let A, B be F-algebras graded by subgroups of G. If M is a G-graded free (A,B)-bimodule, we describe the G-graded polynomial identities of the triangular algebra of M and, in case the field F has characteristic zero, we provide the description of its G-graded cocharacters by means of the graded cocharacters of A and B.