Related papers: An exotic II$_1$ factor without property Gamma
We study Cartan subalgebras in the context of amalgamated free product II$_1$ factors and obtain several uniqueness and non-existence results. We prove that if $\Gamma$ belongs to a large class of amalgamated free product groups (which…
Using an extension of techniques of Ozawa and Popa, we give an example of a non-amenable strongly solid $\rm{II}_1$ factor $M$ containing an "exotic" maximal abelian subalgebra $A$: as an $A$,$A$-bimodule, $L^2(M)$ is neither coarse nor…
We prove that for any free ergodic probability measure preserving action \F_n \actson (X,\mu) of a free group on n generators \F_n, 2 \leq n \leq \infty, the associated group measure space II_1 factor $L^\infty(X) \rtimes \F_n$ has…
Voiculescu's random matrix model for freeness is extended to the non-Gaussian case and also the case of constant block diagonal matrices. Thus we are able to investigate free products of free group factors with matrix algebras and with the…
We give sufficient conditions, in terms of the existence of unbounded derivations satisfying certain properties, which ensure that a II$_1$ factor $M$ is prime or has at most one Cartan subalgebra. For instance, we prove that if there…
We construct inner amenable groups G with infinite conjugacy classes and such that the associated II_1 factor does not have property Gamma of Murray and von Neumann. This solves a problem posed by Effros in 1975.
We investigate Cartan subalgebras in nontracial amalgamated free product von Neumann algebras $M_1 \ast_B M_2$ over an amenable von Neumann subalgebra $B$. First, we settle the problem of the absence of Cartan subalgebra in arbitrary free…
We prove that if $\Gamma$ is an icc irreducible lattice in a product of connected non-compact rank one simple Lie groups with finite center, then the II$_1$ factor $L(\Gamma)$ is prime. In particular, we deduce that the II$_1$ factors…
We obtain an estimate of free entropy of generators in a type ${II}_1$-factor $\mc{M}$ which has a subfactor $\mc{N}$ of finite index with a subalgebra $\mc{P}=\mc{P}_1\vee\mc{P}_2\subset\mc{N}$ where $\mc{P}_1=\mc{R}_1'\cap\mc{P}$,…
We show that a free product of a II_1-factor and a finite von Neumann algebra with amalgamation over a finite dimensional subalgebra is always a II_1-factor, and provide an algorithm for describing it in terms of free products (with…
In the context of Free Probability Theory, we study two different constructions that provide new examples of factors of type ${\rm II_1}$ with prescribed fundamental group. First we investigate state-preserving group actions on the almost…
The interpolated free group factors L(F_r), 1 < r <= \infty, are defined and proofs of their properties with respect to compression by projections and taking free products are proved. Hence it follows that all the free group factor are…
We introduce a framework allowing for key aspects of deformation/rigidity theory to be used in the study of continuous model theory of II$_1$ factors. Using this framework, we solve several well-known open problems in the area. For example,…
One of the earliest invariants introduced in the study of finite von Neumann algebras is the property Gamma of Murray and von Neumann. In this note we prove that it is not possible to classify separable $\rm{II}_1$ factors satisfying the…
We prove that there exist uncountably many separable II$_1$ factors whose ultrapowers (with respect to arbitrary ultrafilters) are non-isomorphic. In fact, we prove that the families of non-isomorphic II$_1$ factors originally introduced by…
Using Voiculsecu's free entropy, it is shown that the free group factors L(F_n) lack property C of Popa and that they lack finite multiplicity abelian subalgebras. Property C is an assymptotic commutivity property.
We provide a fairly large class of II$_1$ factors $N$ such that $M=N\bar{\otimes}R$ has a unique McDuff decomposition, up to isomorphism, where $R$ denotes the hyperfinite II$_1$ factor. This class includes all II$_1$ factors…
We prove that II$_1$ factors $M$ have a unique (up to unitary conjugacy) cross-product type decomposition around ``core subfactors'' $N \subset M$ satisfying the property HT and a certain ``torsion freeness'' condition. In particular, this…
In this paper, we investigate several structural properties for crossed product ${\rm II_1}$ factors $M$ arising from free Bogoljubov actions associated with orthogonal representations $\pi : G \to \mathcal O(H_\mathbf R)$ of arbitrary…
A variant of Gromov's notion of measure equivalence for groups has been introduced for II$_1$ factors under different names. We propose the terminology of W*-correlated II$_1$ factors. We prove rigidity results up to W*-correlations for…