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Research Article | Open Access

Lie n-centralizers of generalized matrix algebras

He Yuan( ), Zhuo Liu
College of Mathematics and Computer, Jilin Normal University, Siping 136000, China
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Abstract

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.

Keywords

Lie n-centralizergeneralized matrix algebrageneralized Lie n-derivation
CLC number: 16W25, 47B47

References

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AIMS Mathematics
Volume 8 Issue 6,
June 2023
Pages 14609-14622
DOI: 10.3934/math.2023747

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Cite this article:
Yuan H, Liu Z. Lie n-centralizers of generalized matrix algebras. AIMS Mathematics, 2023, 8(6): 14609-14622. https://doi.org/10.3934/math.2023747

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Received: 24 February 2023
Revised: 30 March 2023
Accepted: 07 April 2023
Published: 15 June 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)