Chinese Annals of Mathematics, Series B

, Volume 39, Issue 5, pp 817–828 | Cite as

Lie Triple Derivations on von Neumann Algebras



Let \(\mathcal{A}\) be a von Neumann algebra with no central abelian projections. It is proved that if an additive map δ : \(\mathcal{A}\)\(\mathcal{A}\) satisfies δ([[a, b], c]) = [[δ(a), b], c]+[[a, δ(b)], c]+ [[a, b], δ(c)] for any a, b, c\(\mathcal{A}\) with ab = 0 (resp. ab = P, where P is a fixed nontrivial projection in \(\mathcal{A}\)), then there exist an additive derivation d from \(\mathcal{A}\) into itself and an additive map f : \(\mathcal{A}\)\(\mathcal{Z}_\mathcal{A}\) vanishing at every second commutator [[a, b], c] with ab = 0 (resp. ab = P) such that δ(a) = d(a) + f(a) for any a\(\mathcal{A}\).


Derivations Lie triple derivations von Neumann algebras 

2000 MR Subject Classification

16W25 47B47 


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The author wishes to give his thanks to the referees and the editor for their helpful comments and suggestions.


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Copyright information

© Fudan University and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsXidian UniversityXi’anChina
  2. 2.School of Mathematical SciencesFudan UniversityShanghaiChina

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