• 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}
}
© 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. 

Reducible operators in non-Γ type II1 factors

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

Examples of property (T) II$_1$ factors with trivial fundamental group

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

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

New examples of Property (T) factors with trivial fundamental group and unique prime factorization

In this paper we provide new examples of property (T) group factors with trivial fundamental group thereby providing more evidence towards Popa's conjecture on triviality of fundamental groups for

O A ] 9 J un 2 00 8 DIVISIBLE OPERATORS IN VON NEUMANN ALGEBRAS

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

W*-representations of subfactors and restrictions on the Jones index

. 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

Classification of regular subalgebras of the hyperfinite II1 factor

Quantifying metric approximations of discrete groups

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

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

References

SHOWING 1-10 OF 30 REFERENCES

Entropy and index for subfactors

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

Markov traces on universal Jones algebras and subfactors of finite index

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

Random matrices, amalgamated free products and subfactors of the von Neumann algebra of a free group, of noninteger index

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

On the existence of central sequences in subfactors

We prove a relative version of [Co 1, Theorem 2.1 ] for a pair of type III-factors N c M. This gives a list of necessary and sufficient conditions for the existence of nontrivial central sequences of

CLASSIFICATION OF INJECTIVE FACTORS

The fundamental results of A. Connes which determine a complete set of isomorphism classes for most injectlve factors are discussed in detail. After some introductory remarks which lay the foundation

Interpolated free group factors.

The interpolated free group factors L(F_r), 1 < r <= \infty, are defined and proofs of their properties with respect to compression by projections and taking free products are proved. Hence it

A problem on the II₁-factors of Fuchsian groups

We discuss a problem concerning the von Neumann algebra W ∗ λ (Γ) of a Fuchsian group Γ which is finitely generated and non elementary. The problem is to find how such an algebra is related to the

On the method of constructing irreducible finite index subfactors of Popa.

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

Classification of amenable subfactors of type II

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