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Yang, Yuan; Zhang, Jianhua

The second nonlinear mixed bi-skew Lie triple derivations on factor von Neumann algebras. (English) Zbl 07916622

Quaest. Math. 47, No. 7, 1403-1412 (2024).
Summary: Let \(\mathcal{M}\) be a factor von Neumann algebra with \(\dim\mathcal{M} \geq 1\). In this paper, it is shown that if a map \(\phi : \mathcal{M} \to \mathcal{M}\) satisfies \(\phi ([[A, B], C]_\diamond) = [[\phi (A), B], C]_\diamond + [[A, \phi (B)], C]_\diamond + [[A, B], \phi (C)]_\diamond\) for all \(A, B, C \in \mathcal{M}\), then \(\phi\) is an additive \(\ast\)-derivation, where \([A, B]_\diamond = AB^\ast - BA^\ast\).

MSC:

16W25 Derivations, actions of Lie algebras
46L10 General theory of von Neumann algebras

Keywords:

second mixed bi-skew Lie triple products; additive \(\ast\)-derivation; factor von Neumann algebra
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Full Text: DOI

References:

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