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Algebras and Representation Theory

, Volume 20, Issue 2, pp 335–354 | Cite as

Higher Auslander Correspondence for Dualizing R-Varieties

  • Osamu Iyama
  • Gustavo Jasso
Article
  • 119 Downloads

Abstract

Let R be a commutative artinian ring. We extend higher Auslander correspondence from Artin R-algebras of finite representation type to dualizing R-varieties. More precisely, for a positive integer d, we show that a dualizing R-variety is d-abelian if and only if it is a d-Auslander dualizing R-variety if and only if it is equivalent to a d-cluster-tilting subcategory of the category of finitely presented modules over a dualizing R-variety.

Keywords

Artin algebra Dualizing R-variety Auslander algebra Higher Auslander–Reiten theory Cluster-tilting D-abelian category 

Mathematics Subject Classification (2010)

16G10 18A25 

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© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Graduate School of MathematicsNagoya UniversityNagoyaJapan
  2. 2.Mathematisches InstitutUniversität BonnBonnGermany

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