Constructions of symmetric separable equivalences and their applications

2025/08/20 by Sun, Juxiang, Zhao, Guoqiang
#16D20 #16E10 #16E30 #16G10 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2508.14401

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.

Citations

• Separable equivalences, finitely generated cohomology and finite tensor categories
• Frobenius bimodules and flat-dominant dimensions
• The dominant dimension of cohomological Mackey functors
• The representation dimension of Hecke algebras and symmetric groups
• Derived equivalences and stable equivalences of Morita type, I
• Syzygy modules for quasi k-Gorenstein rings

Related

• New invariants of stable equivalences of algebras
• Ortho-symmetric modules, Gorenstein algebras and derived equivalences
• Finitistic and Representation Dimensions
• Gorenstein categories and separable equivalences
• Mirror-reflective algebras and Tachikawa's second conjecture