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 I₁. 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm132-1-5,
author = {Ajda Fo\v sner and Feng Wei and Zhankui Xiao},
title = {Nonlinear Lie-type derivations of von Neumann algebras and related topics},
journal = {Colloquium Mathematicae},
volume = {131},
year = {2013},
pages = {53-71},
zbl = {1306.47047},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm132-1-5}
}
Ajda Fošner; Feng Wei; Zhankui Xiao. Nonlinear Lie-type derivations of von Neumann algebras and related topics. Colloquium Mathematicae, Tome 131 (2013) pp. 53-71. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm132-1-5/