0-Calabi-Yau Configurations and Finite Auslander-Reiten Quivers of Gorenstein Orders

TL;DR

This paper revisits Wiedemann's classification of Auslander-Reiten quivers for representation-finite Gorenstein orders, providing a simpler proof and new descriptions of configurations using 2-Brauer relations.

Contribution

It offers a simplified proof of Wiedemann's classification and introduces a new way to describe configurations via 2-Brauer relations.

Findings

Simplified proof of Wiedemann's classification

Configurations described using 2-Brauer relations

Enhanced understanding of Auslander-Reiten quivers in Gorenstein orders

Abstract

We will revisit Wiedemann's classification of Auslander-Reiten quivers of representation-finite Gorenstein orders in this paper. We give a simpler proof of his result in which he described the Auslander-Reiten quiver of a representation-finite Gorenstein order in terms of a Dynkin diagram, a configuration and an automorphism group. A key notion in his result is configurations described in terms of Brauer relations with so-called Stra{\ss}eneigenschaft. We show that configurations can be described in terms of $2$-Brauer relations very briefly.