• Corpus ID: 253447111

# An upgrading theorem for properly proximal von Neumann algebras

@inproceedings{Ding2022AnUT,
title={An upgrading theorem for properly proximal von Neumann algebras},
author={Changying Ding and Srivatsav Kunnawalkam Elayavalli},
year={2022}
}
• Published 10 November 2022
• Mathematics
Using computations in the bidual of $\mathbb{B}(L^2M)$ 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 $L\Gamma$ where $\Gamma$ is an infinite group that is biexact relative to a finite family of subgroups $\{\Lambda_i\}_{i\in I}$ such that each $\Lambda_i$ is almost malnormal in $\Gamma$. As an application we obtain…
1 Citations
. 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

## References

SHOWING 1-10 OF 38 REFERENCES

• Mathematics
• 2008
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
We discuss different mixing properties for triples of finite von Neumann algebras $B\subset N\subset M$, and we introduce families of triples of groups $H<K<G$ whose associated von Neumann algebras
• Mathematics
Annales Scientifiques de l'École Normale Supérieure
• 2021
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
• Mathematics
Journal of Operator Theory
• 2018
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
We introduce the notion of L2-rigidity for von Neumann algebras, a generalization of property (T) which can be viewed as an analogue for the vanishing of 1-cohomology into the left regular
• Mathematics
• 2019
This paper gives a free entropy theoretic perspective on amenable absorption results for free products of tracial von Neumann algebras. In particular, we give the first free entropy proof of Popa's
We consider crossed product II1 factors $M = N\rtimes_{\sigma}G$, with G discrete ICC groups that contain infinite normal subgroups with the relative property (T) and σ trace preserving actions of G
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
Let $${(M, \varphi) = (M_1, \varphi_1) * (M_2, \varphi_2)}$$(M,φ)=(M1,φ1)∗(M2,φ2) be a free product of arbitrary von Neumann algebras endowed with faithful normal states. Assume that the centralizer
• 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