Covering techniques in Auslander-Reiten theory

TL;DR

This paper introduces covering functors in Auslander-Reiten theory for finite dimensional algebras and applies them to analyze irreducible morphisms and radical powers in module categories.

Contribution

It develops covering functors over mesh categories of Auslander-Reiten components and uses them to study morphism compositions in relation to radical powers.

Findings

Covering functors are constructed for Auslander-Reiten components.

The relationship between irreducible morphisms and radical powers is clarified.

Applications to the structure of module categories are demonstrated.

Abstract

Given a finite dimensional algebra over a perfect field the text introduces covering functors over the mesh category of any modulated Auslander-Reiten component of the algebra. This is applied to study the composition of irreducible morphisms between indecomposable modules in relation with the powers of the radical of the module category.