Lie triple maps on generalized matrix algebras (2103.15172v1)

Abstract: In this article, we introduce the notion of Lie triple centralizer as follows. Let $\mathcal{A}$ be an algebra, and $\phi:\mathcal{A}\to\mathcal{A}$ be a linear mapping. we say $\phi$ is a Lie triple centralizer whenever $\phi([[a,b],c])=[[\phi(a),b],c]$ for all $a,b,c\in\mathcal{A}$. Then we characterize the general form of Lie triple centralizers on generalized matrix algebra $\mathcal{U}$ and under some mild conditions on $\mathcal{U}$, we present the necessary and sufficient conditions for Lie triple centralizers to be proper. As an application of our results, we characterize generalized Lie triple derivations on generalized matrix algebras.