SIMPLE-MINDED SYSTEMS IN STABLE MODULE CATEGORIES

Simple-minded systems (s.m.s.'s) in stable module categories are defined by orthogonality and generating properties so that the images of the simple modules under a stable equivalence form such a system. Under stable equivalences s.m.s.'s are shown to be invariant; thus, the set of all s.m.s.'s is an invariant of a stable module category. The s.m.s.'s of several classes of algebras are described and connections to the Auslander-Reiten conjecture are pointed out.