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].