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Nonlinear generalized Lie triple derivation on triangular algebras

ABSTRACT Let ℛ be a commutative ring with identity and let 𝔄 = Tri(𝒜,ℳ,ℬ) be a triangular algebra consisting of unital algebras 𝒜,ℬ over ℛ and an (𝒜,ℬ)-bimodule ℳ which is faithful as a left 𝒜-module as well as a right ℬ-module. In this paper, we prove that under certain assumptions every nonlinear generalized Lie triple derivation GL:𝔄→𝔄 is of the form GL = δ+τ, where δ:𝔄→𝔄 is an additive generalized derivation on 𝔄 and τ is a mapping from 𝔄 into its center which annihilates all Lie triple products [[x,y],z].