Self-injective algebras with hereditary stable slice

TL;DR

This paper characterizes the structure of certain finite-dimensional self-injective algebras by analyzing their Auslander-Reiten quivers with hereditary stable slices, providing a classification in this specific context.

Contribution

It offers a complete description of self-injective algebras with hereditary stable slices in their Auslander-Reiten quivers, advancing the understanding of their structure.

Findings

Classification of self-injective algebras with hereditary stable slices

Structural description of their Auslander-Reiten quivers

Identification of key properties related to hereditary slices

Abstract

We determine the structure of all finite-dimensional self-injective algebras over a field whose Auslander-Reiten quiver admits a hereditary stable slice.