Strongly solid group factors which are not interpolated free group factors

Details Strongly solid group factors which are not interpolated free group factors Strongly solid group factors which are not interpolated free group factors

2009-01-25

arxiv.org/abs/0901.3866v4

Math. Ann. 346 (2010), 969-989

Mathematics

Operator Algebras

20 pages

Scientific paper

We give examples of non-amenable ICC groups $\Gamma$ with the Haagerup property, weakly amenable with constant $\Lambda_{\cb}(\Gamma) = 1$, for which we show that the associated ${\rm II_1}$ factors $L(\Gamma)$ 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 $\Gamma$, $L(\Gamma)$ is not isomorphic to any interpolated free group factor $L(\F_t)$, for $1 < t \leq \infty$.

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