Strongly solid group factors which are not interpolated free group factors

Abstract

We give examples of non-amenable ICC groups $\Gamma$ with the Haagerup property, weakly amenable with constant $Λ_{\cb}(Γ) = 1$, for which we show that the associated $\mathrm{I}{\mathrm{I}}_1$ 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 $1<t\le \infty$.

20 pages

References in corpus (3)

• Construction of type $\mathrm{I}{\mathrm{I}}_1$ factors with prescribed countable fundamental group
• On a class of II_1 factors with at most one Cartan subalgebra II
• Cocycle Superrigidity for Profinite Actions of Property (T) Groups

Cited by in corpus (8)

• Approximation properties and absence of Cartan subalgebra for free Araki-Woods factors
• On the structural theory of II_1 factors of negatively curved groups, II: Actions by product groups
• Strong solidity of group factors from lattices in SO(n,1) and SU(n,1)
• Amalgamated free product type III factors with at most one Cartan subalgebra
• Structure of $\mathrm{I}{\mathrm{I}}_1$ factors arising from free Bogoljubov actions of arbitrary groups
• Strongly solid $\mathrm{I}{\mathrm{I}}_1$ factors with an exotic MASA
• Strong solidity of free Araki-Woods factors
• Orthogonal free quantum group factors are strongly 1-bounded