Geodesic
Nonlinear Lie-type derivations of von Neumann algebras and related topics
Ajda Fošner 1   ; Feng Wei 2   ; Zhankui Xiao 3
1 Faculty of Management University of Primorska Cankarjeva 5 SI-6104 Koper, Slovenia
2 School of Mathematics Beijing Institute of Technology Beijing, 100081, P.R. China
3 School of Mathematical Sciences Huaqiao University Quanzhou, Fujian, 362021, P.R. China
Colloquium Mathematicum, Tome 132 (2013) no. 1, pp. 53-71 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $\mathcal {A}$ 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.
DOI : 10.4064/cm132-1-5
Keywords: motivated powerful elegant works miers mainly study nonlinear lie type derivations von neumann algebras mathcal von neumann algebra without abelian central summands type shown every nonlinear lie n derivation mathcal has standard form expressed sum additive derivation central valued mapping which annihilates each n commutator nbsp mathcal several potential research topics related work presented

Ajda Fošner  1   ; Feng Wei  2   ; Zhankui Xiao  3

1 Faculty of Management University of Primorska Cankarjeva 5 SI-6104 Koper, Slovenia
2 School of Mathematics Beijing Institute of Technology Beijing, 100081, P.R. China
3 School of Mathematical Sciences Huaqiao University Quanzhou, Fujian, 362021, P.R. China 
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     title = {Nonlinear {Lie-type} derivations of von {Neumann} algebras and related topics},
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Ajda Fošner; Feng Wei; Zhankui Xiao. Nonlinear Lie-type derivations of von Neumann algebras and related topics. Colloquium Mathematicum, Tome 132 (2013) no. 1, pp. 53-71. doi: 10.4064/cm132-1-5

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