Research Article

Lie triple centralizers on generalized matrix algebras

Published in: Quaestiones Mathematicae
Volume 46 , issue 2 , 2023 , pages: 281–300

DOI: 10.2989/16073606.2021.2013972

Author(s): Behrooz Fadaee University of Kurdistan, Iran , Hoger Ghahramani University of Kurdistan, Iran , Wu Jing Fayetteville State University, USA

Keywords: 16W25 , 47B47 , 15A78 , 16W10 , Lie centralizer , Lie triple centralizer , generalized Lie triple derivation , generalized matrix algebra

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Abstract

In this article, we introduce the notion of Lie triple centralizer as follows. Let be an algebra, and be a linear mapping. We say that ϕ is a Lie triple centralizer whenever for all . Then we characterize the general form of Lie triple centralizers on a generalized matrix algebra and under some mild conditions on we present the necessary and suﬃcient conditions for a Lie triple centralizer to be proper. As an application of our results, we characterize generalized Lie triple derivations on generalized matrix algebras.

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