The automatic additivity of $\xi -$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 $\xi -$Lie derivation ($\xi \ne 1$) on $\mathcal{M}$ is an additive derivation.

12 pages