The automatic additivity of $ξ-$Lie derivations on von Neumann algebras

Abstract

Let ${\mathcal M}$ be a von Neumann algebra with no central summands of type I$_1$. It is shown that every nonlinear $ξ-$Lie derivation ($ξ\neq 1$) on $\mathcal M$ is an additive derivation.

12 pages