# Wydawnictwa / Czasopisma IMPAN / Colloquium Mathematicum / Wszystkie zeszyty

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

### Tom 132 / 2013

Colloquium Mathematicum 132 (2013), 53-71 MSC: 47B47, 46L57. DOI: 10.4064/cm132-1-5

#### Streszczenie

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.

#### Autorzy

• Ajda FošnerFaculty of Management
University of Primorska
Cankarjeva 5
SI-6104 Koper, Slovenia
e-mail
• Feng WeiSchool of Mathematics
Beijing Institute of Technology
Beijing, 100081, P.R. China
e-mail
e-mail
• Zhankui XiaoSchool of Mathematical Sciences
Huaqiao University
Quanzhou, Fujian, 362021, P.R. China
e-mail

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