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Research Article | Open Access

Local Lie derivations of generalized matrix algebras

Dan Liu1( ), Jianhua Zhang2, Mingliang Song1
School of Mathematical Sciences, Jiangsu Second Normal University, Nanjing 210013, China
College of Mathematics and Statistics, Shaanxi Normal University, Xi'an 710062, China
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Abstract

In this paper, we investigate local Lie derivations of a certain class of generalized matrix algebras and show that, under certain conditions, every local Lie derivation of a generalized matrix algebra is a sum of a derivation and a linear central-valued map vanishing on each commutator. The main result is then applied to full matrix algebras and unital simple algebras with nontrivial idempotents.

Keywords

local Lie derivationLie derivationgeneralized matrix algebrafull matrix algebra
CLC number: 15A78, 17B40, 47L35

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AIMS Mathematics
Volume 8 Issue 3,
March 2023
Pages 6900-6912
DOI: 10.3934/math.2023349

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Cite this article:
Liu D, Zhang J, Song M. Local Lie derivations of generalized matrix algebras. AIMS Mathematics, 2023, 8(3): 6900-6912. https://doi.org/10.3934/math.2023349

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Received: 20 September 2022
Revised: 21 December 2022
Accepted: 27 December 2022
Published: 15 March 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)