Tensoring Auslander-Reiten sequences with modules

Abstract

Let a : 0→ A→ B→ R→0 be the Auslander-Reiten sequence for the trivial module R over a group algebra RG. Auslander and Carlson characterized RG-modules M which have the property that the tensor product M ⊗ a is, up to projective summands, the Auslander-Reiten sequence for M. In this paper, we look at the tensor product of an arbitrary Auslander-Reiten sequence with a module, and we give a generalization of the result of Auslander and Carlson.