Lie triple centralizers on generalized matrix algebras

AbstractAbstractIn 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.Mathematics Subject Classification (2020): 16W2547B4715A7816W10Key words: Lie centralizerLie triple centralizergeneralized Lie triple derivationgeneralized matrix algebra