Auslander correspondence

TL;DR

This paper explores Auslander correspondence through higher-dimensional Auslander-Reiten theory, providing homological characterizations of Auslander algebras and connecting them to representation dimension and non-commutative resolutions.

Contribution

It offers new homological characterizations of Auslander algebras and addresses a question posed by M. Artin, linking the theory to broader concepts in algebraic geometry.

Findings

Homological characterizations of Auslander algebras

Answer to M. Artin's question

Connections to non-commutative crepant resolutions

Abstract

We study Auslander correspondence from the viewpoint of higher dimensional Auslander-Reiten theory on maximal orthogonal subcategories. We give homological characterizations of Auslander algebras, especially an answer to a question of M. Artin. They are also closely related to Auslander's representation dimension of artin algebras and Van den Bergh's non-commutative crepant resolutions of Gorenstein singularities.