Nonlinear lie-type derivations of von neumann algebras and related topics

Ajda Fošner; Feng Wei; Zhankui Xiao

doi:10.4064/cm132-1-5

Nonlinear lie-type derivations of von neumann algebras and related topics

Ajda Fošner, Feng Wei^*, Zhankui Xiao

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

42 Citations (Scopus)

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 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.

Original language	English
Pages (from-to)	53-71
Number of pages	19
Journal	Colloquium Mathematicum
Volume	132
Issue number	1
DOIs	https://doi.org/10.4064/cm132-1-5
Publication status	Published - 2013

Keywords

Generalized matrix al- gebra
Lie n-derivation
Nest algebra
Von neumann algebra

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Nonlinear lie-type derivations of von neumann algebras and related topics

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