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.
Citation: He Yuan, Zhuo Liu. Lie $ n $-centralizers of generalized matrix algebras[J]. AIMS Mathematics, 2023, 8(6): 14609-14622. doi: 10.3934/math.2023747
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.
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He Yuan, Zhuo Liu. Lie $ n $-centralizers of generalized matrix algebras[J]. AIMS Mathematics, 2023, 8(6): 14609-14622. doi: 10.3934/math.2023747
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