• Corpus ID: 214773920

# Free-independent sequences in type II1 factors and related problems

@inproceedings{Popa2019FreeindependentSI,
title={Free-independent sequences in type II1 factors and related problems},
author={Sorin Popa and Sorin Popa and Sorin Popa},
year={2019}
}
• Published 2019
© Société mathématique de France, 1995, tous droits réservés. L’accès aux archives de la collection « Astérisque » (http://smf4.emath.fr/ Publications/Asterisque/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
14 Citations

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A famous question of Halmos asks whether every operator on a separable infinite dimensional Hilbert space is a norm limit of reducible operators. In [30], Voiculescu gave this problem an affirmative

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In this article we provide the first examples of property (T) $\rm II_1$ factors $\mathcal N$ with trivial fundamental group, $\mathcal F (\mathcal N)=1$. Our examples arise as group factors

### Reducible operators in non-$\Gamma$ type ${\rm II}_1$ factors

• Mathematics
• 2019
A famous question of Halmos asks whether every operator on a separable infinite dimensional Hilbert space is a norm limit of reducible operators. In [30] , Voiculescu gave this problem an affirmative

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Relativizing an idea from multiplicity theory, we say that an element x of a von Neumann algebra M is n-divisible if W (x) ∩ M unitally contains a factor of type In. We decide the density of the

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. A W ∗ -representation of a II 1 subfactor N ⊂ M with ﬁnite Jones index, [ M : N ] < ∞ , is a non-degenerate commuting square embedding of N ⊂ M into an inclusion of atomic von Neumann algebras ⊕ i

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Journal de Mathématiques Pures et Appliquées
• 2020

### Quantifying metric approximations of discrete groups

• Mathematics, Computer Science
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The approach generalizes classical isoperimetric profiles of amenable groups and recently introduced functions quantifying residually finite groups as well as many other metric approximations such as weakly sofic, weakly hyperlinear, and linear sofimations.

### New examples of W$^*$ and C$^*$-superrigid groups

• Mathematics
• 2020
A group $G$ is called $W^*$-superrigid (resp. $C^*$-superrigid) if it is completely recognizable from its von Neumann algebra $L(G)$ (resp. reduced $C^*$-algebra $C_r^*(G)$). Developing new technical

### Asymptotic Orthogonalization of Subalgebras in II$_1$ Factors

• S. Popa
• Mathematics
Publications of the Research Institute for Mathematical Sciences
• 2019
Let $M$ be a II$_1$ factor with a von Neumann subalgebra $Q\subset M$ that has infinite index under any projection in $Q'\cap M$ (e.g., $Q$ abelian; or $Q$ an irreducible subfactor with infinite

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• Mathematics
• 1986
Soit M un facteur de type II 1 de trace normalise τ et N⊂M un sous-facteur. On demontre que l'indice [M:N] est fini si et seulement si M est un module projectif finiment genere sur N et que si c'est

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We construct one parameter families of inclusions of nonhyperfinite type II1 factorsNs⊂Ms, with trivial relative commutant (Ns)′∩Ms=ℂ and with the Jones' index [Ms∶Ns]=s ranging over the sets∈{4

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The Göttingen State and University Library provides access to digitized documents strictly for noncommercial educational, research and private purposes and makes no warranty with regard to their use

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Let US(Q) be the universal Jones algebra associated to a finite von Neumann algebra Q and Rs c R be the Jones subfactors, s € {4cos2 \\n > 3} U [4, oo). We consider for any von Neumann subalgebra Qo

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0. Introduction 1. Basics of the theory of subfactors 1.1. General inclusions 1.2. Subfactors of finite index 1.3. The s tandard invariant (the paragroup) 1.4. Core and model inclusions 2. A