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Singular equivalences and Auslander-Reiten conjecture

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arxiv 2011.02729 v1 pith:GQ4DCZT4 submitted 2020-11-05 math.RT math.RA

Yiping Chen , Wei Hu , Yongyun Qin , Ren Wang This is my paper · ORCID
classification math.RTmath.RA
keywords conjectureauslander-reitenequivalencessingularaccordinglyadjointalgebraalgebras
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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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