Nonlinear mixed skew Jordan-Lie-type higher derivations on $ \ast $-algebras

He Yuan; Xiaokui Li; He Yuan; Xiaokui Li

doi:10.3934/era.2026287

Electronic Research Archive

2026, Volume 34, Issue 9: 6558-6572. doi: 10.3934/era.2026287

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Research article

Nonlinear mixed skew Jordan-Lie-type higher derivations on $ \ast $-algebras

He Yuan ,
Xiaokui Li ^,

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

Received: 08 May 2026 Revised: 28 June 2026 Accepted: 27 July 2026 Published: 31 July 2026

The notion of a nonlinear mixed skew Jordan-Lie-type higher derivation on unital $ \ast $-algebras is introduced, which combines the skew Jordan product with skew Lie-type higher derivations. Under conditions satisfied by prime $ \ast $-algebras, factor von Neumann algebras, and standard operator algebras, it is proved that every nonlinear mixed skew Jordan-Lie-type higher derivation on a unital $ \ast $-algebra is an additive higher $ \ast $-derivation.
- skew Jordan product,
- skew Lie product,
- $ \ast $-algebra,
- higher derivation,
- $ \ast $-derivation
Citation: He Yuan, Xiaokui Li. Nonlinear mixed skew Jordan-Lie-type higher derivations on $ \ast $-algebras[J]. Electronic Research Archive, 2026, 34(9): 6558-6572. doi: 10.3934/era.2026287

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Abstract

The notion of a nonlinear mixed skew Jordan-Lie-type higher derivation on unital $ \ast $-algebras is introduced, which combines the skew Jordan product with skew Lie-type higher derivations. Under conditions satisfied by prime $ \ast $-algebras, factor von Neumann algebras, and standard operator algebras, it is proved that every nonlinear mixed skew Jordan-Lie-type higher derivation on a unital $ \ast $-algebra is an additive higher $ \ast $-derivation.

References

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