Context-Equivalence of Algebras with Involutions.

Abstract

Morita equivalence is the central concept of celebrated Morita theory. Two algebras are Morita equivalent if their categories of modules are equivalent.

A Morita context is a useful technical concept that allows one to establish Morita equivalence. Based on this concept B. Muller introduced the notion of context-equivalence in 1972. Later S. A. Amitsur showed that although the context-equivalence is coarser than Morita equivalence, many algebraic properties are still invariant relative to this new equivalence.

In this talk we will we will present a version of context-equivalence suitable for the category of algebras with involution. The main result is a criterion of context-equivalence of such algebras.