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arXiv · 2103.15172

Lie triple maps on generalized matrix algebras

Behrooz Fadaee
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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.

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BibTeXRIS

Behrooz Fadaee. 2021-03-28. Lie triple maps on generalized matrix algebras. https://arxiv.org/abs/2103.15172

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