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On triangle equivalences of stable categories

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

preprint2018arXivOpen access
Zhenxing DiZhongkui LiuJiaqun Wei
math.RTmath.ACmath.AGmath.KTmath.RA
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Zhenxing DiZhongkui LiuJiaqun Wei

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