New invariants of stable equivalences of algebras

Abstract: We show that the Auslander-Reiten conjecture on stable equivalences holds true for principal centralizer matrix algebras over an arbitrary field and for Frobenius-finite algebras over an algebraically closed field, that stable equivalences of algebras with positive $\nu$-dominant dimensions preserve stable equivalences of their Frobenius parts, and that the delooping levels, $\phi$-dimensions and $\psi$-dimensions are invariants of stable equivalences of Artin algebras without nodes.