Nonlinear 2-local Lie n-derivations of von Neumann algebras

Abstract

Let M be a finite von Neumann algebra with no central summands of type I 1. We show that each nonlinear 2-local Lie n-derivation δ : M → M with n ≥ 3 is of the form d + h, where d : M → M is a linear derivation and h is a homogeneous central-valued mapping which annihilates each ( n − 1 ) -th commutator of M .