2-Local derivations on matrix algebras over commutative regular algebras

Shavkat Ayupov; Karimbergen Kudaybergenov; Amir Alauadinov

doi:10.1016/j.laa.2013.04.013

2-Local derivations on matrix algebras over commutative regular algebras

Shavkat Ayupov
, Karimbergen Kudaybergenov^*
, Amir Alauadinov

^*Corresponding author for this work

National University of Uzbekistan named after Mirzo Ulugbek
Abdus Salam International Centre for Theoretical Physics
Karakalpak State University

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

14 Scopus citations

Abstract

The paper is devoted to 2-local derivations on matrix algebras over commutative regular algebras. We give necessary and sufficient conditions on a commutative regular algebra to admit 2-local derivations which are not derivations. We prove that every 2-local derivation on a matrix algebra over a commutative regular algebra is a derivation. We apply these results to 2-local derivations on algebras of measurable and locally measurable operators affiliated with type I von Neumann algebras.

Original language	English
Pages (from-to)	1294-1311
Number of pages	18
Journal	Linear Algebra and Its Applications
Volume	439
Issue number	5
DOIs	https://doi.org/10.1016/j.laa.2013.04.013
State	Published - 1 Sep 2013
Externally published	Yes

Keywords

2-Local derivation
Derivation
Matrix algebra
Regular algebra

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10.1016/j.laa.2013.04.013

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N2 - The paper is devoted to 2-local derivations on matrix algebras over commutative regular algebras. We give necessary and sufficient conditions on a commutative regular algebra to admit 2-local derivations which are not derivations. We prove that every 2-local derivation on a matrix algebra over a commutative regular algebra is a derivation. We apply these results to 2-local derivations on algebras of measurable and locally measurable operators affiliated with type I von Neumann algebras.

AB - The paper is devoted to 2-local derivations on matrix algebras over commutative regular algebras. We give necessary and sufficient conditions on a commutative regular algebra to admit 2-local derivations which are not derivations. We prove that every 2-local derivation on a matrix algebra over a commutative regular algebra is a derivation. We apply these results to 2-local derivations on algebras of measurable and locally measurable operators affiliated with type I von Neumann algebras.

KW - 2-Local derivation

KW - Derivation

KW - Matrix algebra

KW - Regular algebra

UR - https://www.scopus.com/pages/publications/84879232684

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ER -

2-Local derivations on matrix algebras over commutative regular algebras

Abstract

Keywords

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