Non-global nonlinear Lie n-derivations on unital algebras with idempotents

Let T be a unital algebra with nontrivial idempotents. For any (Formula Presented), define p₁ (s₁) = s₁, p₂ (s₁, s₂) = [s₁, s₂ ] and p_n (s₁, s₂, …, s_n) = [p_n−1 (s₁, s₂, …, s_n−1), s_n ] for all integers n ≥ 3. In the present article, it is shown that if a map (Formula Presented) satisfies (Formula Presented) for all (Formula Presented) with s₁ s₂ · · · s_n = 0, then (Formula Presented) for all s, (Formula Presented), and under some mild assumptions φ is of the form δ + τ, where (Formula Presented) is an additive derivation and (Formula Presented) is a map such that τ(p_n (s₁, s₂, …, s_n)) = 0 for all (Formula Presented) with s₁ s₂ · · · s_n = 0. The above results are then applied to certain special classes of unital algebras, namely triangular algebras, full matrix algebras and algebra of all bounded linear operators.