Generalized Lie $ n $-derivations on generalized matrix algebras

Shan Li; Kaijia Luo; Jiankui Li; Shan Li; Kaijia Luo; Jiankui Li

doi:10.3934/math.20241424

AIMS Mathematics

2024, Volume 9, Issue 10: 29386-29403. doi: 10.3934/math.20241424

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Research article

Generalized Lie $ n $-derivations on generalized matrix algebras

Shan Li ¹,
Kaijia Luo ^{2
,
,},
Jiankui Li ^{3
,
,}

1.
Department of Mathematics, Jiangsu University of Technology, Changzhou, 213001, China
2.
Institute of Mathematics, Hangzhou Dianzi University, Hangzhou, 310018, China
3.
Department of Mathematics, East China University of Science and Technology, Shanghai, 200237, China

Received: 22 July 2024 Revised: 08 October 2024 Accepted: 11 October 2024 Published: 17 October 2024
MSC : 47B47, 47C15

Let $ \mathcal{G} $ be a generalized matrix algebra. We show that under certain conditions, each generalized Lie $ n $-derivation associated with a linear map on $ \mathcal{G} $ is a sum of a generalized derivation and a central map vanishing on all $ (n-1) $-th commutators and is also a sum of a generalized inner derivation and a Lie $ n $-derivation. As an application, generalized Lie $ n $-derivations on von Neumann algebras are characterized.
- generalized Lie $ n $-derivation,
- Lie $ n $-derivation,
- generalized matrix algebra
Citation: Shan Li, Kaijia Luo, Jiankui Li. Generalized Lie $ n $-derivations on generalized matrix algebras[J]. AIMS Mathematics, 2024, 9(10): 29386-29403. doi: 10.3934/math.20241424

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Abstract

Let $ \mathcal{G} $ be a generalized matrix algebra. We show that under certain conditions, each generalized Lie $ n $-derivation associated with a linear map on $ \mathcal{G} $ is a sum of a generalized derivation and a central map vanishing on all $ (n-1) $-th commutators and is also a sum of a generalized inner derivation and a Lie $ n $-derivation. As an application, generalized Lie $ n $-derivations on von Neumann algebras are characterized.

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