# Local and 2-Local derivations on noncommutative Arens algebras

Source: [Local and 2-Local derivations on noncommutative Arens algebras](<https://www.sota2.com/research/paper/68fa4f651e209131ce962f9e>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T10:16:43.177Z

Authors: Sh. A. Ayupov, K. K. Kudaybergenov, B. O. Nurjanov, A. K. Alauatdinov

Published: 2011-10-07T14:59:54.000Z

## Abstract

The paper is devoted to so-called local and 2-local derivations on the noncommutative Arens algebra $L^\\omega(M, \\tau)$ associated with a von Neumann algebra $M$ and a faithful normal semi-finite trace $\\tau.$ We prove that every 2-local derivation on $L^\\omega(M, \\tau)$ is a spatial derivation, and if $M$ is a finite von Neumann algebra, then each local derivation on $L^\\omega(M, \\tau)$ is also a spatial derivation and every 2-local derivation on $M$ is in fact an inner derivation.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1110.1557>)

[PDF](<https://arxiv.org/pdf/1110.1557.pdf>)