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Auslander-Gorenstein algebras and precluster tilting
- Source :
- Adv. Math. 326 (2018), 200--240
- Publication Year :
- 2016
-
Abstract
- We generalize the notions of $n$-cluster tilting subcategories and $\tau$-selfinjective algebras into $n$-precluster tilting subcategories and $\tau_n$-selfinjective algebras, where we show that a subcategory naturally associated to $n$-precluster tilting subcategories has a higher Auslander--Reiten theory. Furthermore, we give a bijection between $n$-precluster tilting subcategories and $n$-minimal Auslander--Gorenstein algebras, which is a higher dimensional analog of Auslander--Solberg correspondence (Auslander--Solberg, 1993) as well as a Gorenstein analog of $n$-Auslander correspondence (Iyama, 2007). The Auslander--Reiten theory associated to an $n$-precluster tilting subcategory is used to classify the $n$-minimal Auslander--Gorenstein algebras into four disjoint classes. Our method is based on relative homological algebra due to Auslander--Solberg.<br />Comment: 32 pages, final published version. The terminology `n-minimal Auslander-Gorenstein algebra' is used
Details
- Database :
- arXiv
- Journal :
- Adv. Math. 326 (2018), 200--240
- Publication Type :
- Report
- Accession number :
- edsarx.1608.04179
- Document Type :
- Working Paper