Related papers: Bernoulli actions of type III_1 and L^2-cohomology

We determine the Krieger type of nonsingular Bernoulli actions $G \curvearrowright \prod_{g \in G} (\{0,1\},\mu_g)$. When $G$ is abelian, we do this for arbitrary marginal measures $\mu_g$. We prove in particular that the action is never of…

We prove that every infinite amenable group admits Bernoulli actions of any possible Krieger type, including type $II_\infty$ and type $III_0$. We obtain this result as a consequence of general results on the ergodicity and Krieger type of…

We prove that if $G$ is a countable, discrete group having infinite, normal subgroups with the relative property (T), then the Bernoulli shift action of $G$ on ${\underset g \in G \to \Pi} (X_0, \mu_0)_g$ for $(X_{0},\mu_{0})$ an arbitrary…

Given a countable amenable group G and 0 < L < 1, we give an elementary construction of a type-III:L Bernoulli group action. In the case where G is the integers, we show that our nonsingular Bernoulli shifts have independent and identically…

We show that the principal algebraic actions of countably infinite groups associated to lopsided elements in the integral group ring satisfying some orderability condition are Bernoulli.

We give examples of principal algebraic actions of the noncommutative free group $F$ of rank two, as well as other groups, by automorphisms of a connected compact abelian group for which there is an explicit measurable isomorphism to a…

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,…

We prove that if a countable group $\Gamma$ contains infinite commuting subgroups $H, H'\subset \Gamma$ with $H$ non-amenable and $H'$ ``weakly normal'' in $\Gamma$, then any measure preserving $\Gamma$-action on a probability space which…

We study strongly outer actions of discrete groups on C*-algebras in relation to (non)amenability. In contrast to related results for amenable groups, where uniqueness of strongly outer actions on the Jiang-Su algebra is expected, we show…

In this article we study cocycles of discrete countable groups with values in l^2(G) and the ring of affiliated operators UG. We clarify properties of the first cohomology of a group G with coefficients in l^2(G) and answer several…

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 study actions of countable discrete groups which are amenable in the sense that there exists a mean on X which is invariant under the action of G. Assuming that G is nonamenable, we obtain structural results for the stabilizer subgroups…

Let $G$ be an amenable discrete countable infinite group, $A$ a finite set, and $(\mu_g)_{g\in G}$ a family of probability measures on $A$ such that $\inf_{g\in G}\min_{a\in A}\mu_g(a)>0$. It is shown (among other results) that if the…

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…

It is shown that each non-compact locally compact second countable non-(T) group $G$ possesses non-strongly ergodic weakly mixing IDPFT Poisson actions of arbitrary Krieger's type. These actions are amenable if and only if $G$ is amenable.…

We show that, for countable sofic groups, a Bernoulli action with infinite entropy base has infinite entropy with respect to every sofic approximation sequence. This builds on the work of Lewis Bowen in the case of finite entropy base and…

Let $G$ be a semisimple Lie group with Haar measure $\mu$ and let $\Gamma$ be an irreducible lattice in $G$. For $g\in G$, we consider left translation $L_g$ acting on $(G\backslash\Gamma,\mu)$. We show that if $L_g$ is $K$ (which is…

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…

We give many examples of algebraic actions which are factors of Bernoulli shifts. These include certain harmonic models over left orderable groups of large enough growth, as well as algebraic actions associated to certain lopsided elements…

A measure preserving action of a countably infinite group \Gamma is called totally ergodic if every infinite subgroup of \Gamma acts ergodically. For example, all mixing and mildly mixing actions are totally ergodic. This note shows that if…