Auslander correspondence
Osamu Iyama

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.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Algebra and Geometry · Advanced Topics in Algebra
