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The automatic additivity of $\xi-$Lie derivations on von Neumann algebras
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classification
math.FAquant-ph
keywords
derivationmathcalneumannadditiveadditivityalgebraalgebrasautomatic
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 ($\xi\neq 1$) on $\mathcal M$ is an additive derivation.
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