Lie $n$-centralizers of generalized matrix algebras

Source abstract

<abstract><p>In this paper, we introduce the notion of Lie $n$-centralizers. We then give a description of Lie $n$-centralizers on a generalized matrix algebra and present the necessary and sufficient conditions for a Lie $n$-centralizer to be proper. As applications, we determine generalized Lie $n$-derivations on a generalized matrix algebra and Lie $n$-centralizers of some operator algebras.</p></abstract>