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Research Article | Open Access

Generalized Lie n-derivations on generalized matrix algebras

Shan Li1, Kaijia Luo2( ), Jiankui Li3( )
Department of Mathematics, Jiangsu University of Technology, Changzhou, 213001, China
Institute of Mathematics, Hangzhou Dianzi University, Hangzhou, 310018, China
Department of Mathematics, East China University of Science and Technology, Shanghai, 200237, China
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Abstract

Let G be a generalized matrix algebra. We show that under certain conditions, each generalized Lie n-derivation associated with a linear map on G is a sum of a generalized derivation and a central map vanishing on all (n−1)-th commutators and is also a sum of a generalized inner derivation and a Lie n-derivation. As an application, generalized Lie n-derivations on von Neumann algebras are characterized.

Keywords

generalized Lie n-derivationLie n-derivationgeneralized matrix algebra
CLC number: 47B47, 47C15

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AIMS Mathematics
Volume 9 Issue 10,
October 2024
Pages 29386-29403
DOI: 10.3934/math.20241424

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Cite this article:
Li S, Luo K, Li J. Generalized Lie n-derivations on generalized matrix algebras. AIMS Mathematics, 2024, 9(10): 29386-29403. https://doi.org/10.3934/math.20241424

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Received: 22 July 2024
Revised: 08 October 2024
Accepted: 11 October 2024
Published: 15 October 2024
©2024 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)