Nonlinear $*$-Lie higher derivations on factor von Neumann algebras

Abstract

Let $mathcal M$ be a factor von Neumann algebra. It is shown that every nonlinear $*$-Lie higher derivation $D={phi_{n}}_{ninmathbb{N}}$ on $mathcal M$ is additive. In particular, if $mathcal M$ is infinite type $I$ factor, a concrete characterization of $D$ is given.