Constructions of symmetrical separable equivalences and their applications
Colloquium Mathematicum
MSC: Primary 16G10; Secondary 16E10
DOI: 10.4064/cm9716-4-2026
Published online: 21 September 2026
Abstract
Let $\varLambda $ and $\varGamma $ be symmetrically separably equivalent Artin algebras. We prove that there exist symmetrical separable equivalences between certain endomorphism algebras. As applications, we provide several methods to construct symmetrical separable equivalences from given ones and discuss when the rigidity dimension is invariant under symmetrical separable equivalence. Moreover, we show that symmetrical separable equivalence preserves the Frobenius-finite type, an Auslander-type condition, the (strong) Nakayama conjecture and the Auslander–Gorenstein conjecture.
