Local Lie $n$-derivations on certain algebras

Abstract

We prove that each local Lie $n$-derivation is a Lie $n$-derivation under mild assumptions on the unital algebras with a nontrivial idempotent. As applications, we obtain descriptions of local Lie $n$-derivations on generalized matrix algebras, triangular algebras, nest algebras, von Neumann algebras, and the algebras of locally measurable operators affiliated with a von Neumann algebra.