Generalized bi-skew Lie-type higher derivations on $ \ast $-algebras

Chuqi Jia; He Yuan; Ke Shi; Chuqi Jia; He Yuan; Ke Shi

doi:10.3934/math.2026963

AIMS Mathematics

2026, Volume 11, Issue 8: 23921-23942. doi: 10.3934/math.2026963

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Research article

Generalized bi-skew Lie-type higher derivations on $ \ast $-algebras

College of Mathematics, Jilin Normal University, Siping, Jilin 136000, China

Received: 15 June 2026 Revised: 12 July 2026 Accepted: 29 July 2026 Published: 05 August 2026
MSC : 16W25, 47B47

Let $ \mathcal{A} $ be a unital $ \ast $-algebra over the complex field $ \mathbb {C} $, and let $ G = \{ G _m\} _{m \in \mathbb{N}} $ be a nonlinear generalized bi-skew Lie $ n $-higher derivation on $ \mathcal{A} $. In this paper, we prove that under certain conditions, $ G $ is an additive generalized higher $ \ast $-derivation on $ \mathcal{A} $. As applications, we characterize nonlinear generalized bi-skew Lie $ n $-higher derivations on some classical unital $ \ast $-algebras, such as von Neumann algebras.
- bi-skew Lie product,
- $ \ast $-algebra,
- generalized bi-skew Lie $ n $-higher derivation,
- generalized higher $ \ast $-derivation
Citation: Chuqi Jia, He Yuan, Ke Shi. Generalized bi-skew Lie-type higher derivations on $ \ast $-algebras[J]. AIMS Mathematics, 2026, 11(8): 23921-23942. doi: 10.3934/math.2026963

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Abstract

Let $ \mathcal{A} $ be a unital $ \ast $-algebra over the complex field $ \mathbb {C} $, and let $ G = \{ G _m\} _{m \in \mathbb{N}} $ be a nonlinear generalized bi-skew Lie $ n $-higher derivation on $ \mathcal{A} $. In this paper, we prove that under certain conditions, $ G $ is an additive generalized higher $ \ast $-derivation on $ \mathcal{A} $. As applications, we characterize nonlinear generalized bi-skew Lie $ n $-higher derivations on some classical unital $ \ast $-algebras, such as von Neumann algebras.

References

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