Nonlinear Lie-type derivations of von Neumann algebras and related topics
Volume 132 / 2013
Colloquium Mathematicum 132 (2013), 53-71
MSC: 47B47, 46L57.
DOI: 10.4064/cm132-1-5
Abstract
Motivated by the powerful and elegant works of Miers (1971, 1973, 1978) we mainly study nonlinear Lie-type derivations of von Neumann algebras. Let $\mathcal {A}$ be a von Neumann algebra without abelian central summands of type $I_1$. It is shown that every nonlinear Lie $n$-derivation of $\mathcal {A}$ has the standard form, that is, can be expressed as a sum of an additive derivation and a central-valued mapping which annihilates each $(n-1)$th commutator of $\mathcal {A}$. Several potential research topics related to our work are also presented.
