On triangle equivalences of stable categories
Zhenxing Di, Zhongkui Liu, Jiaqun Wei
TL;DR
This paper uses approximation theory to realize certain subfactor triangulated categories as quotients, extending classical equivalences and characterizations for Gorenstein rings and algebras.
Contribution
It introduces a new realization of Iyama and Yoshino's subfactor categories as triangulated quotients, extending Buchweitz's triangle equivalence to more general rings.
Findings
Recovered results of Iyama, Yang, and the third author.
Extended Buchweitz's equivalence to Noetherian rings.
Provided characterizations for Gorenstein rings and algebras.
Abstract
We apply the Auslander-Buchweitz approximation theory to show that the Iyama and Yoshino's subfactor triangulated category can be realized as a triangulated quotient. Applications of this realization go in three directions. Firstly, we recover both a result of Iyama and Yang and a result of the third author. Secondly, we extend the classical Buchweitz's triangle equivalence from Iwanaga-Gorenstein rings to Noetherian rings. Finally, we obtain the converse of Buchweitz's triangle equivalence and a result of Beligiannis, and give characterizations for Iwanaga-Gorenstein rings and Gorenstein algebras
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