Maximal amenable subalgebras of von Neumann algebras associated with hyperbolic groups

@article{Boutonnet2013MaximalAS,
title={Maximal amenable subalgebras of von Neumann algebras associated with hyperbolic groups},
author={R'emi Boutonnet and Alessandro Carderi},
journal={Mathematische Annalen},
year={2013},
volume={367},
pages={1199-1216}
}
• Published 22 October 2013
• Mathematics
• Mathematische Annalen
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 amenable subalgebras in II$$_1$$1 factors. We also prove similar maximal amenability results for direct products of relatively hyperbolic groups and orbit equivalence relations arising from measure-preserving actions of such groups.
• Mathematics
• 2014
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
• Mathematics
Geometric and Functional Analysis
• 2015
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
• 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
• Mathematics
Journal of Functional Analysis
• 2022
• Mathematics
• 2018
We show that certain amenable subgroups inside Ã2-groups are singular in the sense of Boutonnet and Carderi. This gives a new family of examples of singular group von Neumann subalgebras. We also
Ge (2003) asked the question whether LF∞ can be embedded in to LF2 as a maximal subfactor. We answer it affirmatively in three different approaches, all containing the same key ingredient: the
• Mathematics
• 2022
. We say that a countable discrete group Γ satisﬁes the non-commutative Margulis (NCM) property if every Γ - invariant von Neumann subalgebra M in L (Γ) is of the form L (Λ) for some normal subgroup
• Mathematics
• 2020
We show that certain amenable subgroups inside $$\widetilde {A}_2$$-groups are singular in the sense of Boutonnet and Carderi. This gives a new family of examples of singular group von Neumann
• Mathematics
• 2015
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
• L. Bowen
• Mathematics
Ergodic Theory and Dynamical Systems
• 2017
Consider a measured equivalence relation acting on a bundle of hyperbolic metric spaces by isometries. We prove that every aperiodic hyperfinite subequivalence relation is contained in a unique

References

SHOWING 1-10 OF 22 REFERENCES

To every subfactor planar algebra was associated a II1 factor with a canonical abelian subalgebra generated by the cup tangle. Using Popa's approximative orthogonality property, we show that this cup
• D. Osin
• Mathematics
Int. J. Algebra Comput.
• 2006
It is shown that if an element g ∈ G has infinite order and is not conjugate to an element of some Hλ, λ ∈ Λ, then the (unique) maximal elementary subgroup containing g is hyperbolically embedded into G, which allows us to prove that if G is boundedly generated, then G is elementary or Hλ = G for some λ → Λ.
Abstract We prove that a δ-hyperbolic group for δ < ½ is a free product F * G 1 * … * Gn where F is a free group of finite rank and each Gi is a finite group.
We present families of pairs of finite von Neumann algebras $A\subset M$ where $A$ is a maximal injective masa in the type $\mathrm{II}_1$ factor $M$ with separable predual. Our results make use of
This paper defines the boundary of a relatively hyperbolic group, and shows that the limit set of any geometrically finite action of the group is equivariantly homeomorphic to this boundary, and generalizes a result of Tukia for geometRically finite kleinian groups.
• Mathematics
• 2011
We introduce and study the notions of hyperbolically embedded and very rotating families of subgroups. The former notion can be thought of as a generalization of the peripheral structure of a
We suggest a new approach to the study of relatively hyperbolic groups based on relative isoperimetric inequalities. Various geometric, algebraic, and algorithmic properties are discussed.