Geodesic
Nonlinear Lie-type derivations of von Neumann algebras and related topics
Ajda Fošner1 ; Feng Wei2 ; Zhankui Xiao3
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.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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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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. http://geodesic.mathdoc.fr/articles/10.4064/cm132-1-5/

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