Nonlinear Lie type Derivations of Von Neumann Algebras

Abstract

Let $A$ be a von Neumann algebra with no central summands of type $I_1$. We will show that every nonlinear Lie $n$-derivation on $A$ is of the standard form, i.e. it can be expressed as a sum of an additive derivation and a central-valued mapping which annihilates each $(n-1)$-th commutator of $A$.

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