Bulletin of the Iranian Mathematical Society

, Volume 45, Issue 2, pp 569–581 | Cite as

Nonlinear Generalized Lie n-Derivations on von Neumann Algebras

  • Xiaoxue Feng
  • Xiaofei QiEmail author
Original Paper


Let \({\mathcal {M}}\) be a von Neumann algebra without central summands of type \(I_1\). Assume that \(G:{{\mathcal {M}}}\rightarrow {{\mathcal {M}}}\) is a nonlinear map. It is shown that G is a generalized Lie n-derivation (\(n\ge 2\)) if and only if \(G(A)=\varphi (A)+\tau (A)\) holds for all \(A\in {{\mathcal {M}}}\), where \(\varphi :{\mathcal M}\rightarrow {{\mathcal {M}}}\) is an additive generalized derivation and \(\tau :{{\mathcal {M}}}\rightarrow {{\mathcal {Z}}}({{\mathcal {M}}})\) is a central-valued map annihilating all \((n-1)\)th commutators. This generalizes some related known results.


Generalized Lie n-derivations Lie n-derivations Lie derivations von Neumann algebras 

Mathematics Subject Classification

47B47 47B49 



The authors wish to give their thanks to the referees for careful reading and many valued comments.


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Copyright information

© Iranian Mathematical Society 2018

Authors and Affiliations

  1. 1.Department of MathematicsShanxi UniversityTaiyuanPeople’s Republic of China

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