• Corpus ID: 253447111

An upgrading theorem for properly proximal von Neumann algebras

  title={An upgrading theorem for properly proximal von Neumann algebras},
  author={Changying Ding and Srivatsav Kunnawalkam Elayavalli},
. Using computations in the bidual of B ( L 2 M ) we develop a technique at the von Neumann algebra level to upgrade relative proper proximality to full proper proximality in the presence of some mixing and non co-amenability assumptions. This is used to classify subalgebras of L Γ where Γ is an infinite group that is biexact relative to a finite family of subgroups { Λ i } i ∈ I such that each Λ i is almost malnormal in Γ. As an application we obtain an absorption theorem for free products in… 
1 Citations

First $\ell^2$-Betti numbers and proper proximality

. We show that for a countable exact group, having positive first ℓ 2 -Betti number implies proper proximality in this sense of [BIP21]. This is achieved by showing a cocycle super-rigidty result for



Maximal amenable von Neumann subalgebras arising from maximal amenable subgroups

We provide a general criterion to deduce maximal amenability of von Neumann subalgebras LΛ ⊂ LΓ arising from amenable subgroups Λ of discrete countable groups Γ. The criterion is expressed in terms


  • A. Ioana
  • Mathematics
    Proceedings of the International Congress of Mathematicians (ICM 2018)
  • 2019
We survey some of the progress made recently in the classification of von Neumann algebras arising from countable groups and their measure preserving actions on probability spaces. We emphasize

Maximal amenability of the generator subalgebra in q-Gaussian von Neumann algebras

In this article, we give explicit examples of maximal amenable subalgebras of the $q$-Gaussian algebras, namely, the generator subalgebra is maximal amenable inside the $q$-Gaussian algebras for real

Properly proximal groups and their von Neumann algebras

We introduce a wide class of countable groups, called properly proximal, which contains all non-amenable bi-exact groups, all non-elementary convergence groups, and all lattices in non-compact

Amenable absorption in amalgamated free product von Neumann algebras

We investigate the position of amenable subalgebras in arbitrary amalgamated free product von Neumann algebras M = M1 * B M2. Our main result states that under natural analytic assumptions, any

The cup subalgebra has the absorbing amenability property

Consider an inclusion of diffuse von Neumann algebras A c M . We say that A c M has the absorbing amenability property if for any diffuse subalgebra B c A and any amenable intermediate algebra B c D

On a class of II1 factors with at most one Cartan subalgebra, II

This is a continuation of our previous paper studying the structure of Cartan subalgebras of von Neumann factors of type ${\rm II}_1$. We provide more examples of ${\rm II}_1$ factors having either

A Topology for Operator Modules overW*-Algebras

Abstract Given a von Neumann algebraRon a Hilbert space H , the so-calledR-topology is introduced into B( H ), which is weaker than the norm and stronger than the ultrastrong operator topology. A

Bass-Serre rigidity results in von Neumann algebras

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

Maximal amenable subalgebras of von Neumann algebras associated with hyperbolic groups

We prove that for any infinite, maximal amenable subgroup H in a hyperbolic group G, the von Neumann subalgebra LH is maximal amenable inside LG. It provides many new, explicit examples of maximal