@article{Houdayer2010StructuralRF,
author={Cyril Houdayer},
journal={Journal of the Institute of Mathematics of Jussieu},
year={2010},
volume={9},
pages={741 - 767}
}
• Cyril Houdayer
• Published 7 December 2008
• Mathematics
• Journal of the Institute of Mathematics of Jussieu
Abstract We show that for any type III1 free Araki–Woods factor $\mathcal{M}$ = (HR, Ut)″ associated with an orthogonal representation (Ut) of R on a separable real Hilbert space HR, the continuous core M = $\mathcal{M}$ ⋊σR is a semisolid II∞ factor, i.e. for any non-zero finite projection q ∈ M, the II1 factor qM q is semisolid. If the representation (Ut) is moreover assumed to be mixing, then we prove that the core M is solid. As an application, we construct an example of a non-amenable…
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## References

SHOWING 1-10 OF 52 REFERENCES
Amalgamated free products of weakly rigid factors and calculation of their symmetry groups
• Mathematics
• 2005
We consider amalgamated free product II1 factors M = M1*BM2*B… and use “deformation/rigidity” and “intertwining” techniques to prove that any relatively rigid von Neumann subalgebra Q ⊂ M can be
Strong rigidity of II1 factors arising from malleable actions of w-rigid groups, I
We consider crossed product II1 factors $M = N\rtimes_{\sigma}G$, with G discrete ICC groups that contain infinite normal subgroups with the relative property (T) and σ trace preserving actions of G
Construction of type II1 factors with prescribed countable fundamental group
Abstract In the context of Free Probability Theory, we study two different constructions that provide new examples of factors of type II1 with prescribed countable fundamental group. First we
Bass-Serre rigidity results in von Neumann algebras
• Mathematics
• 2008
We obtain new Bass-Serre type rigidity results for ${\rm II_1}$ equivalence relations and their von Neumann algebras, coming from free ergodic actions of free products of groups on the standard
On a class of type $II_1$ factors with Betti numbers invariants
We prove that a type II1 factor M can have at most one Cartan subalgebra A satisfying a combination of rigidity and compact approximation properties. We use this result to show that within the class
On a class of $\mathrm{II}_1$ factors with at most one Cartan subalgebra
• Mathematics
• 2007
We prove that the normalizer of any diffuse amenable subalgebra of a free group factor $L(\Bbb F_r)$ generates an amenable von Neumann subalgebra. Moreover, any II$_1$ factor of the form \$Q \vt
On Some Free Products of Von Neumann Algebras which are Free Araki–Woods Factors
We prove that certain free products of factors of type I and other von Neumann algebras with respect to nontracial, almost periodic states are almost periodic free Araki–Woods factors. In particular,
Some estimates for non-microstates free entropy dimension with applications to q-semicircular families
We give a general estimate for the nonmicrostates free entropy dimension δ*(X 1 ,…X n ). If X 1 ,…X n generate a diffuse von Neumann algebra, we prove that δ*X 1 ,…X n ≥ 1. In the case that X 1 ,…,X
Conne’s bicentralizer problem and uniqueness of the injective factor of type III1
In Connes' fundamental work "Classification of injective factors" [7], it is proved that injective factors of type III,t, 2 . 1 on a separable Hilbert space are completely classified by their "smooth