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Research Article | Open Access

Characterizations of local Lie derivations on von Neumann algebras

Guangyu An1( ), Xueli Zhang1, Jun He2, Wenhua Qian3( )
Department of Mathematics, Shaanxi University of Science and Technology, Xi'an 710021, China
Department of Mathematics, Anhui Polytechnic University, Wuhu 241000, China
School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China
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Abstract

In this paper, we prove that every local Lie derivation on von Neumann algebras is a Lie derivation; and we show that if M is a type I von Neumann algebra with an atomic lattice of projections, then every local Lie derivation on L S ( M ) is a Lie derivation.

Keywords

Lie derivationlocal Lie derivationvon Neumann algebralocally measurable operator
CLC number: 46L50, 46L57, 47L35

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AIMS Mathematics
Volume 7 Issue 5,
May 2022
Pages 7519-7527
DOI: 10.3934/math.2022422

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Cite this article:
An G, Zhang X, He J, et al. Characterizations of local Lie derivations on von Neumann algebras. AIMS Mathematics, 2022, 7(5): 7519-7527. https://doi.org/10.3934/math.2022422

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Received: 21 October 2021
Revised: 13 December 2021
Accepted: 21 December 2021
Published: 15 May 2022
©2022 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)