Auslander correspondence

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.

29 pages. Final Version. To appear in Adv. Math

Cited by in corpus (73)

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• Trivial Maximal 1-Orthogonal Subcategories For Auslander's 1-Gorenstein Algebras
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• Nakayama Algebras which are Higher Auslander Algebras
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• Higher Auslander correspondence for exact categories
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• Gabriel-Quillen embedding for $n$-exact categories
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