Nonlinear Lie-type derivations of von Neumann algebras and related topics

Ajda Fošner; Feng Wei; Zhankui Xiao

Colloquium Mathematicae (2013)

  • Volume: 132, Issue: 1, page 53-71
  • ISSN: 0010-1354

Abstract

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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.

How to cite

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Ajda Fošner, Feng Wei, and Zhankui Xiao. "Nonlinear Lie-type derivations of von Neumann algebras and related topics." Colloquium Mathematicae 132.1 (2013): 53-71. <http://eudml.org/doc/286302>.

@article{AjdaFošner2013,
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.},
author = {Ajda Fošner, Feng Wei, Zhankui Xiao},
journal = {Colloquium Mathematicae},
keywords = {Lie -derivation; von Neumann algebra; generalized matrix algebra; nest algebra},
language = {eng},
number = {1},
pages = {53-71},
title = {Nonlinear Lie-type derivations of von Neumann algebras and related topics},
url = {http://eudml.org/doc/286302},
volume = {132},
year = {2013},
}

TY - JOUR
AU - Ajda Fošner
AU - Feng Wei
AU - Zhankui Xiao
TI - Nonlinear Lie-type derivations of von Neumann algebras and related topics
JO - Colloquium Mathematicae
PY - 2013
VL - 132
IS - 1
SP - 53
EP - 71
AB - 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.
LA - eng
KW - Lie -derivation; von Neumann algebra; generalized matrix algebra; nest algebra
UR - http://eudml.org/doc/286302
ER -

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