More on Lie Derivations of Generalized Matrix Algebras

TL;DR

This paper studies Lie derivations on generalized matrix algebras, providing new characterizations and conditions for their properness, building on and extending previous theoretical work in the area.

Contribution

It offers a new approach to constructing Lie derivations and establishes sufficient conditions for their properness in generalized matrix algebras.

Findings

Provides a direct proof for known results in Lie derivations

Characterizes when Lie derivations are proper

Offers new sufficient conditions for properness

Abstract

Motivated by the Cheung's elaborate work [Linear Multilinear Algebra, 51 (2003), 299-310], we investigate the construction of a Lie derivation on a generalized matrix algebra and apply it to give a characterization for such a Lie derivation to be proper. Our approach not only provides a direct proof for some known results in the theory, but also it presents several sufficient conditions assuring the properness of Lie derivations on certain generalized matrix algebras.