Nonlinear Lie Triple Higher Derivations on Triangular Algebras by Local Actions: A New Perspective

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Let R be a commutative ring with unity and T be a triangular algebra over R. Let a sequence Δ={δn}n∈N of nonlinear mappings δn:T→T is a Lie triple higher derivation by local actions satisfying the equation. Under some mild conditions on T, we prove in this paper that every Lie triple higher derivation by local actions on the triangular algebras is proper. As an application, we shall give a characterization of Lie triple higher derivations by local actions on upper triangular matrix algebras and nest algebras, respectively.