Local and 2-local derivations on noncommutative Arens algebras

Shavkat Ayupov; Karimbergen Kudaybergenov; Berdakh Nurjanov; Amir Alauadinov

doi:10.2478/s12175-014-0215-9

Local and 2-local derivations on noncommutative Arens algebras

Shavkat Ayupov^*
, Karimbergen Kudaybergenov
, Berdakh Nurjanov
, Amir Alauadinov

^*Corresponding author for this work

Academy of Sciences of the Republic of Uzbekistan
Abdus Salam International Centre for Theoretical Physics
Karakalpak State University

Research output: Contribution to journal › Article › peer-review

24 Scopus citations

Abstract

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

Original language	English
Pages (from-to)	423-432
Number of pages	10
Journal	Mathematica Slovaca
Volume	64
Issue number	2
DOIs	https://doi.org/10.2478/s12175-014-0215-9
State	Published - Apr 2014
Externally published	Yes

Keywords

2-local derivation
derivation
local derivation
noncommutative Arens algebra
semi-finite trace
von Neumann algebra

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10.2478/s12175-014-0215-9

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title = "Local and 2-local derivations on noncommutative Arens algebras",

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

keywords = "2-local derivation, derivation, local derivation, noncommutative Arens algebra, semi-finite trace, von Neumann algebra",

author = "Shavkat Ayupov and Karimbergen Kudaybergenov and Berdakh Nurjanov and Amir Alauadinov",

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AU - Ayupov, Shavkat

AU - Kudaybergenov, Karimbergen

AU - Nurjanov, Berdakh

AU - Alauadinov, Amir

PY - 2014/4

Y1 - 2014/4

N2 - The paper is devoted to so-called local and 2-local derivations on the noncommutative Arens algebra L ω(M,τ) associated with a von Neumann algebra M and a faithful normal semi-finite trace τ. We prove that every 2-local derivation on L ω(M,τ) is a spatial derivation, and if M is a finite von Neumann algebra, then each local derivation on L ω(M,τ) is also a spatial derivation and every 2-local derivation on M is in fact an inner derivation.

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

KW - 2-local derivation

KW - derivation

KW - local derivation

KW - noncommutative Arens algebra

KW - semi-finite trace

KW - von Neumann algebra

UR - https://www.scopus.com/pages/publications/84899909477

U2 - 10.2478/s12175-014-0215-9

DO - 10.2478/s12175-014-0215-9

M3 - 文章

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SN - 0139-9918

VL - 64

SP - 423

EP - 432

JO - Mathematica Slovaca

JF - Mathematica Slovaca

IS - 2

ER -

Local and 2-local derivations on noncommutative Arens algebras

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Keywords

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