Nonlinear Lie triple derivations of triangular algebras

Abstract

Let 𝒯 be a triangular algebra over a 2-torsion free commutative ring R. In this article, under some mild conditions on 𝒯, we prove that if δ: 𝒯 → 𝒯 is a nonlinear mapping satisfying

for any x, y, z ∈ 𝒯, then δ = d + τ, where d is an additive derivation of 𝒯 and τ: 𝒯 → Z(𝒯) (where Z(𝒯) is the centre of 𝒯) is a map vanishing at Lie triple products [[x, y], z].

Keywords:

• nonlinear Lie triple derivation
• additive derivation
• triangular algebra

AMS Subject Classifications::

• 16W25
• 47B49

Acknowledgements

The authors thank the referee for the very thorough reading of this article and many helpful comments. The first author is supported by the National Natural Science Foundation Grants of China (10971117).