Auslander-Reiten theory revisited

Abstract

We recall several results in Auslander-Reiten theory for finite-dimensional algebras over fields and orders over complete local rings. Then we introduce $n$-cluster tilting subcategories and higher theory of almost split sequences and Auslander algebras there. Several examples are explained.

47 pages, To appear in the Proceeding of the ICRA XII conference, Torun, August 2007

References in corpus (6)

• On triangulated orbit categories
• Calabi-Yau algebras
• Cluster structures for 2-Calabi-Yau categories and unipotent groups
• Acyclic Calabi-Yau categories
• Rigid objects in higher cluster categories
• Relative homology and maximal l-orthogonal modules

Cited by in corpus (14)

• n-representation-finite algebras and twisted fractionally Calabi-Yau algebras
• $n$-cluster tilting subcategories of representation-directed algebras
• Special tilting modules for algebras with positive dominant dimension
• Higher Auslander correspondence for dualizing $R$-varieties
• Higher Auslander's formula
• Higher Auslander-Reiten sequences and $t$-structures
• Skew group algebras of Jacobian algebras
• Tensor products of higher almost split sequences
• Tensor products of n-complete algebras
• Gluing of $n$-cluster tilting subcategories for representation-directed algebras
• $d\mathbb{Z}$-cluster tilting subcategories of singularity categories
• On faithfully balanced modules, F-cotilting and F-Auslander algebras
• $n$-cluster tilting subcategories from gluing systems of representation-directed algebras
• Classification of the d-representation-finite symmetric k-algebras of finite representation type