On triangle equivalences of stable categories
Representation Theory
2020-04-01 v1 Commutative Algebra
Algebraic Geometry
K-Theory and Homology
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
Keywords
Cite
@article{arxiv.1808.00339,
title = {On triangle equivalences of stable categories},
author = {Zhenxing Di and Zhongkui Liu and Jiaqun Wei},
journal= {arXiv preprint arXiv:1808.00339},
year = {2020}
}