On the stable module category of a self-injective algebra

Abstract

LetΛbe a finite-dimensional self-injective algebra. We study thedimensions of spaces of stable homomorphisms between indecomposableΛ-moduleswhich belong to Auslander-Reiten components of the form ZA∞or\textZA_\infty/\langleτ^k\rangle. The results are applied to representations of finitegroups over fields of prime characteristic,especially blocks of wildrepresentation type.