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Strongly solid group factors which are not interpolated free group factors

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Abstract

We give examples of non-amenable infinite conjugacy classes groups Γ with the Haagerup property, weakly amenable with constant Λcb(Γ) = 1, for which we show that the associated II1 factors L(Γ) are strongly solid, i.e. the normalizer of any diffuse amenable subalgebra \({P \subset L(\Gamma)}\) generates an amenable von Neumann algebra. Nevertheless, for these examples of groups Γ, L(Γ) is not isomorphic to any interpolated free group factor L(F t ), for 1 < t ≤  ∞.

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  1. CNRS-ENS Lyon, UMPA UMR 5669, 69364, Lyon cedex 7, France

    Cyril Houdayer

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  1. Cyril Houdayer
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Houdayer, C. Strongly solid group factors which are not interpolated free group factors. Math. Ann. 346, 969–989 (2010). https://doi.org/10.1007/s00208-009-0417-6

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