Self-injective artin algebras without short cycles in the component quiver

TL;DR

This paper classifies all self-injective artin algebras of infinite representation type that have a component quiver free of short cycles, providing a comprehensive structural description.

Contribution

It offers a complete characterization of such algebras, filling a gap in the understanding of their structural properties.

Findings

Identifies conditions for the absence of short cycles in the component quiver.

Provides a classification of all relevant self-injective artin algebras.

Enhances understanding of the structure of infinite representation type algebras.

Abstract

We give a complete description of all self-injective artin algebras of infinite representation type whose component quiver has no short cycles.