Related papers: Bernoulli crossed products without almost periodic…

Crossed products with noncommutative Bernoulli actions were introduced by Connes as the first examples of full factors of type III. This article provides a complete classification of the factors $(P,\phi)^{\mathbb{F}_n} \rtimes…

We prove rigidity and classification results for type III factors given by nonsingular Bernoulli actions of the free groups and more general free product groups. This includes a large family of nonisomorphic Bernoulli crossed products of…

We prove that many, but not all injective factors arise as crossed products by nonsingular Bernoulli actions of the group $\mathbb{Z}$. We obtain this result by proving a completely general result on the ergodicity, type and Krieger's…

We generalize a theorem of Chifan and Ioana by proving that for any, possibly type III, amenable von Neumann algebra $A_0$, any faithful normal state $\varphi_0$ and any discrete group $\Gamma$, the associated Bernoulli crossed product von…

We study the Bernoulli property for a class of partially hyperbolic systems arising from skew products. More precisely, we consider a hyperbolic map $(T,M,\mu)$, where $\mu$ is a Gibbs measure, an aperiodic H\"older continuous cocycle…

We construct an exemple of a full factor $M$ such that its canonical outer modular flow $\sigma^M : \mathbb{R} \rightarrow \mathrm{Out}(M)$ is almost periodic but $M$ has no almost periodic state. This can only happen if the discrete…

We consider group measure space II$_1$ factors $M=L^{\infty}(X)\rtimes\Gamma$ arising from Bernoulli actions of ICC property (T) groups $\Gamma$ (more generally, of groups $\Gamma$ containing an infinite normal subgroup with relative…

Let $\mu_{\lambda}$ be the Bernoulli convolution measure with parameter $\lambda\in(0,1)$. We study the regularity of the function %We prove that $h=h_{\phi}:\lambda\mapsto \int_{\mathbb{R}}\phi(x)\,d\mu_{\lambda}(x)$ for H\"older…

We prove a "unique crossed product decomposition" result for group measure space II_1 factors arising from arbitrary free ergodic probability measure preserving (p.m.p.) actions of groups \Gamma in a fairly large family G, which contains…

We show that if $\Gamma\curvearrowright (X^\Gamma,\mu^\Gamma)$ is a Bernoulli action of an i.c.c. nonamenable group $\Gamma$ which is weakly amenable with Cowling-Haagerup constant $1$, and $\Lambda\curvearrowright(Y,\nu)$ is a free ergodic…

We explore classifiability of crossed products of actions of countable amenable groups on compact, metrizable spaces. It is completely understood when such crossed products are simple, separable, unital, nuclear and satisfy the UCT: these…

We establish a non-commutative version of the Intermediate Factor Theorem for crossed products associated with product lattices. Given an irreducible lattice $\Gamma < G= G_1 \times \dots \times G_d$ in higher rank semisimple algebraic…

We study the notion of permutation stability (or P-stability) for countable groups. Our main result provides a wide class of non-amenable product groups which are not P-stable. This class includes the product group $\Sigma\times\Lambda$,…

Let $R_\infty$ denote the Araki--Woods factor -- the unique separable injective type III$_{1}$ factor. For extremal almost periodic states $\varphi, \psi\in (R_\infty)_*$, we show that if $\Delta_\varphi$ and $\Delta_\psi$ have the same…

We obtain several rigidity results regarding tensor product decompositions of factors. First, we show that any full factor with separable predual has at most countably many tensor product decompositions up to stable unitary conjugacy. We…

We show that the class $\mathscr{B}$, of discrete groups which satisfy the conclusion of Popa's Cocycle Superrigidity Theorem for Bernoulli actions, is invariant under measure equivalence. We generalize this to the setting of discrete…

We study the structure of tensor products of $\mathfrak{gl}(\infty) = \varinjlim \mathfrak{gl}(n)$-modules $\mathbf L(\mathbf \lambda) \otimes \mathbf F$ where $\mathbf L(\mathbf \lambda)$ is a simple integrable highest weight module and…

We provide a simple criterion for a non-singular and conservative Bernouilli action to have a weakly mixing Maharam extension. As an application, we show that every countable amenable group admits a stable type III_1 Bernoulli action,…

Using the continuous decomposition, we classify strongly free actions of discrete amenable groups on strongly amenable subfactors of type III$_\lambda, 0 < \lambda < 1$. Winsl{\o}w's fundamental homomorphism is a complete invariant. This…

In this paper, we give a complete, two-way characterization, of when a noncommutative crossed product $A \rtimes_\lambda G$ is simple, in the case of $G$ being an FC-hypercentral group. This is a large class of amenable groups that contains…