Local Lie derivations of generalized matrix algebras

Dan Liu; Jianhua Zhang; Mingliang Song; Dan Liu; Jianhua Zhang; Mingliang Song

doi:10.3934/math.2023349

AIMS Mathematics

2023, Volume 8, Issue 3: 6900-6912. doi: 10.3934/math.2023349

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Research article

Local Lie derivations of generalized matrix algebras

1.
School of Mathematical Sciences, Jiangsu Second Normal University, Nanjing 210013, China
2.
College of Mathematics and Statistics, Shaanxi Normal University, Xi'an 710062, China

Received: 20 September 2022 Revised: 21 December 2022 Accepted: 27 December 2022 Published: 10 January 2023
MSC : 15A78, 17B40, 47L35

In this paper, we investigate local Lie derivations of a certain class of generalized matrix algebras and show that, under certain conditions, every local Lie derivation of a generalized matrix algebra is a sum of a derivation and a linear central-valued map vanishing on each commutator. The main result is then applied to full matrix algebras and unital simple algebras with nontrivial idempotents.
- local Lie derivation,
- Lie derivation,
- generalized matrix algebra,
- full matrix algebra
Citation: Dan Liu, Jianhua Zhang, Mingliang Song. Local Lie derivations of generalized matrix algebras[J]. AIMS Mathematics, 2023, 8(3): 6900-6912. doi: 10.3934/math.2023349

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Abstract

In this paper, we investigate local Lie derivations of a certain class of generalized matrix algebras and show that, under certain conditions, every local Lie derivation of a generalized matrix algebra is a sum of a derivation and a linear central-valued map vanishing on each commutator. The main result is then applied to full matrix algebras and unital simple algebras with nontrivial idempotents.

References

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