A study on generalized matrix algebras having generalized Lie derivations

Abstract

Let \(\mathfrak{R}\) be a commutative ring with unity. The \(\mathfrak{R}\)-algebra \(\mathfrak{G}=\mathfrak{G}(\mathrm{A}, \mathrm{M}, \mathrm{N}, \mathrm{B})\) is a generalized matrix algebra defined by the Morita context \((\mathrm{A}, \mathrm{B}, \mathrm{M}, \mathrm{N}, \xi_{\mathrm{M}\mathrm{N}}, \Omega_{\mathrm{N}\mathrm{M}}).\) In this article, we study generalized Lie derivation and show that every generalized Lie derivation on a generalized matrix algebra has the standard form under certain assumptions.