Relative stable equivalences of Morita type

Abstract

In the representation theory of finite groups, the stable equivalence of Morita type plays a prominent role. However, except for self-injective algebras, one does not know much on existence of such equivalences between arbitrary algebras. Moreover, this notion seems to be not general enough, to be preserved by classical algebraic constructions. In the paper there is introduced a notion of relative stable equivalence of Morita type. Such an equivalence appears in the context of stable equivalence of Morita type, as is showed in Theorem 0.1.