Related papers: Properly Proximal von Neumann Algebras
We study graph products of groups from the viewpoint of measured group theory. We first establish a full measure equivalence classification of graph products of countably infinite groups over finite simple graphs with no transvection and no…
We prove that weak amenability of a locally compact group imposes a strong condition on its amenable closed normal subgroups. This extends non weak amenability results of Haagerup (1988) and Ozawa--Popa (2010). A von Neumann algebra…
Consider a countable group Gamma acting ergodically by measure preserving transformations on a probability space (X,mu), and let R_Gamma be the corresponding orbit equivalence relation on X. The following rigidity phenomenon is shown: there…
We show that the reduced von Neumann algebras of the free orthogonal and free unitary quantum groups have the Haagerup approximation property. Using this result and a Haagerup-type inequality for these quantum groups due to Vergnioux (J.…
Using an approach emerging from the theory of closable derivations on von Neumann algebras, we exhibit a class of groups CR satisfying the following property: given any groups G_1, G_2 in CR, then any free, ergodic, measure preserving…
It is shown by Houdayer-Isono that a group measure space von Neumann algebra is a full factor if the group is countable discrete and bi-exact, and the action is strongly ergodic, essentially free and non-singular. Recently, bi-exactness for…
In this paper we study various von Neumann algebraic rigidity aspects for the property (T) groups that arise via the Rips construction developed by Belegradek and Osin in geometric group theory \cite{BO06}. Specifically, developing a new…
Amenable actions of locally compact groups on von Neumann algebras are investigated by exploiting the natural module structure of the crossed product over the Fourier algebra of the acting group. The resulting characterisation of…
The aim of the article is to provide characterizations of the Haage-rup property for locally compact, second countable groups in terms of approximations of some non-ergodic invariant states by mixing ones for actions on unital…
We survey Sorin Popa's recent work on Bernoulli actions. The paper was written on the occasion of the Bourbaki seminar. Using very original methods from operator algebras, Sorin Popa has shown that the orbit structure of the Bernoulli…
A topological group $G$ is called extremely amenable if every continuous action of $G$ on a compact space has a fixed point. This concept is linked with geometry of high dimensions (concentration of measure). We show that a von Neumann…
We show that if G is a discrete group which does not have the Haagerup property but does have an unbounded cocycle into a C_0 representation and if G acts on a finite von Neumann algebra B such that the inclusion B \subset (B \rtimes G) has…
The notion of von Neumann equivalence (vNE), which encapsulates both measure equivalence and $W^*$-equivalence, was introduced recently by Jesse Peterson, Lauren Ruth and the author. They showed that many analytic properties, such as…
We give some natural conditions on actions of discrete countable groups on abelian locally compact groups of Lie type that imply factoriality of the group von Neumann algebras of their semidirect products. This allows us to give a fairly…
Using Popa's deformation/rigidity theory, we investigate prime decompositions of von Neumann algebras of the form $L(\mathcal{R})$ for countable probability measure preserving equivalence relations $\mathcal{R}$. We show that…
We investigate the use of Popa's asymptotic orthogonality to establish maximal amenability for amalgamated free product von Neumann algebras. Although new techniques have recently been developed to consider amalgamated free products, we…
This paper includes a series of structural results for von Neumann algebras arising from measure preserving actions by product groups on probability spaces. Expanding upon the methods used earlier by the first two authors \cite{CS}, we…
We introduce inner amenability for discrete p.m.p. groupoids and investigate its basic properties, examples, and the connection with central sequences in the full group of the groupoid or central sequences in the von Neumann algebra…
We show that the orthogonal free quantum groups are not inner amenable and we construct an explicit proper cocycle weakly contained in the regular representation. This strengthens the result of Vaes and the second author, showing that the…
We show that every non-amenable free product of groups admits free ergodic probability measure preserving actions which have relative property (T) in the sense of S.-Popa \cite[Def. 4.1]{Pop06}. There are uncountably many such actions up to…