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Solid von Neumann algebras. (English) Zbl 1072.46040

A von Neumann algebra is said to be diffuse if it does not contain a minimal projection. A von Neumann algebra \(M\) is called solid if for any diffuse von Neumann subalgebra \(A\) in \(M\), the relative commutant \(A'\cap M\) is injective. The main result of the present paper is the following theorem which answers a question of L. Ge [Ann. Math. 147, 143–157 (1998; Zbl 0924.46050)] whether the free group factors are solid.
Theorem: The group von Neumann algebra \(\mathcal L \Gamma\) of a hyperbolic group \(\Gamma\) is solid.

MSC:

46L10 General theory of von Neumann algebras

Citations:

Zbl 0924.46050
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References:

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