Local Lie derivations on certain operator algebras

Liu, Dan; Zhang, Jianhua

doi:10.1215/20088752-0000012x

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Introduction2

More Generally a Linear Map δ Of U Is Called A Lie Derivation If δ([A B]) = [δ(A) B] + [A δ(B)]1

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2018

2024

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Cited by 12 publications

(3 citation statements)

References 22 publications

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“…Later, Chen and Lu [3] proved that each local Lie derivation of nest algebras on Hilbert spaces is a Lie derivation. In [14,15], Liu and Zhang proved that the same is true for local Lie derivations on von Neumann algebras and a certain class of triangular algebras, respectively. The purpose of the present paper is to characterize local Lie derivations of generalized matrix algebras under certain conditions.…”

Section: More Generally a Linear Map δ Of U Is Called A Lie Derivation If δ([A B]) = [δ(A) B] + [A δ(B)]mentioning

confidence: 80%

On local Lie derivations of generalized matrix algebras

Liu

2019

Banach J. Math. Anal.

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Section: More Generally a Linear Map δ Of U Is Called A Lie Derivation If δ([A B]) = [δ(A) B] + [A δ(B)]mentioning

confidence: 80%

On local Lie derivations of generalized matrix algebras

Liu

2019

Banach J. Math. Anal.

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“…[13,Theorem 7.5]). Based on these results, many authors have studied local derivations on operator algebras, for example, see in [2,3,4,5,6,7,8,9,10,11,12,15,16,17,18,19,20,22,23].…”

Section: Introductionmentioning

confidence: 99%

Local derivations on associative and Jordan matrix algebras

Ayupov¹,

Arzikulov²,

Umrzaqov³

2019

UzMJ

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In the present paper we prove that every additive (not necessarily homogenous) local inner derivation on the algebra of matrices over an arbitrary field is an inner derivation, and every local inner derivation on the ring of matrices over a finite ring generated by the identity element or the ring of integers is an inner derivation. We also prove that every additive local inner derivation on the Jordan algebra of symmetric matrices over an arbitrary field is a derivation, and every local inner derivation on the Jordan ring of symmetric matrices over a finite ring generated by the identity element or the ring of integers is a derivation.

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“…In [11], L. Chen and F. Lu prove that every local Lie derivation on nest algebras is a Lie derivation. In [26], D. Liu and J. Zhang prove that under certain conditions, every local Lie derivation on triangular algebras is a Lie derivation. In [20], J.…”

Section: Introductionmentioning

confidence: 99%

Local Lie derivations on von Neumann algebras and algebras of locally measurable operators

He¹,

An²

2018

Preprint

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Let A be a unital associative algebra and M be an A-bimodule. A linear mappingand ϕ is called a local Lie derivation if for every A in A, there exists a Lie derivation ϕ A (depending on A) from A into M such that ϕ(A) = ϕ A (A). 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 atomic lattice of projections, then every local Lie derivation on LS(M) is a Lie derivation.

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Local Lie derivations on certain operator algebras

Cited by 12 publications

References 22 publications

On local Lie derivations of generalized matrix algebras

On local Lie derivations of generalized matrix algebras

Local derivations on associative and Jordan matrix algebras

Local Lie derivations on von Neumann algebras and algebras of locally measurable operators

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