New invariants of stable equivalences of algebras

Abstract

We show that stable equivalences between Artin algebras without nodes preserve homological data that provide upper bounds for finitistic dimension, and that stable equivalences between Artin algebras with positive $\nu$-dominant dimensions induce stable equivalences of their Frobenius parts. As an application of our new methods developed, we verify the Auslander--Reiten conjecture on stable equivalences for two rather different classes of algebras: principal centralizer matrix algebras over arbitrary fields and Frobenius-finite algebras over algebraically closed fields.