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arXiv · 2508.14401

Constructions of symmetric separable equivalences and their applications

Juxiang Sun·Guoqiang Zhao
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Abstract

Let $Λ$ and $Γ$ be symmetrically separably equivalent Artin algebras. We prove that there exist symmetrical separable equivalences between certain endomorphism algebras of modules. As applications, we provide several methods to construct symmetrical separable equivalences from given ones and discuss when the rigidity dimension is an invariant under symmetrical separable equivalences. Moreover, we show that a symmetrical separable equivalence preserves the Frobenius-finite type, Auslander-type condition, the (strong) Nakayama conjecture, the Auslander-Gorenstein conjecture and so on.

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Juxiang Sun, Guoqiang Zhao. 2025-08-20. Constructions of symmetric separable equivalences and their applications. https://arxiv.org/abs/2508.14401

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