On the stable module category of a self-injective algebra

Abstract

Let Λ \Lambda be a finite-dimensional self-injective algebra. We study the dimensions of spaces of stable homomorphisms between indecomposable Λ \Lambda -modules which belong to Auslander-Reiten components of the form Z A ∞ \mathbf {Z}A_\infty or Z A ∞ / ⟨ τ k ⟩ \mathbf {Z}A_\infty /\langle \tau ^k\rangle . The results are applied to representations of finite groups over fields of prime characteristic, especially blocks of wild representation type.