科研之友
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摘要
Motivated by the powerful and elegant works of Miers (1971, 1973, 1978) we mainly study nonlinear Lie-type derivations of von Neumann algebras. Let A be a von Neumann algebra without abelian central summands of type I-1. It is shown that every nonlinear Lie n-derivation of 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 A. Several potential research topics related to our work are also presented.
