A survey on Auslander-Gorenstein algebras

TL;DR

This survey reviews Auslander-Gorenstein algebras, emphasizing recent classification results and their interactions with other algebraic bijections, mainly in the context of finite-dimensional algebras.

Contribution

It compiles recent advances in classifying Auslander-Gorenstein algebras and explores their connections with established algebraic bijections.

Findings

Recent classification results for special classes of Auslander-Gorenstein algebras.

New interactions between Auslander-Reiten bijections and other algebraic bijections.

Enhanced understanding of the structure of finite-dimensional Auslander-Gorenstein algebras.

Abstract

We give a survey on Auslander-Gorenstein algebras with a focus on finite-dimensional algebras. We put an emphasis on recent classification results for special classes of algebras and the newly discovered interactions of the Auslander-Reiten bijection with other well studied bijections in the literature.