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

(16 Feb 2013)  Key: citeulike:12040636

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### 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.