Lie (Jordan) centralizers on generalized matrix algebras

Abstract

Let R be a commutative ring with unit element, A,B be R-algebras, M be an (A,B)-bimodule, and N be a (B,A)-bimodule. The R-algebra G=G(A,M,N,B) is a generalized matrix algebra defined by the Morita context (A,B,M,N,ξMN,ΩNM). In this article, we study Lie (Jordan) centralizer on generalized matrix algebras and obtain the necessary and sufficient conditions for a Lie centralizer map to be proper. Further, we prove that every Jordan centralizer is a centralizer on generalized matrix algebras under certain assumptions.

Topics & Concepts