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arXiv · 2011.02729

Singular equivalences and Auslander-Reiten conjecture

Yiping Chen·Wei Hu·Yongyun Qin·Ren Wang
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Abstract

Auslander-Reiten conjecture, which says that an Artin algebra does not have any non-projective generator with vanishing self-extensions in all positive degrees, is shown to be invariant under certain singular equivalences induced by adjoint pairs, which occur often in matrix algebras, recollements and change of rings. Accordingly, several reduction methods are established to study this conjecture.

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Yiping Chen, Wei Hu, Yongyun Qin, Ren Wang. 2020-11-05. Singular equivalences and Auslander-Reiten conjecture. https://arxiv.org/abs/2011.02729

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