The fundamental group of the von Neumann algebra of a free group with infinitely many generators is $\mathbb{R}_+\slash \{0\}$

@article{Rdulescu1992TheFG,
  title={The fundamental group of the von Neumann algebra of a free group with infinitely many generators is \$\mathbb\{R\}\_+\slash \\{0\\}\$},
  author={Florin Rădulescu},
  journal={Journal of the American Mathematical Society},
  year={1992},
  volume={5},
  pages={517-517}
}
  • F. Rădulescu
  • Published 1 September 1992
  • Mathematics
  • Journal of the American Mathematical Society
In this paper we show that the fundamental group Y of the von Neumann algebra Y(Fo) of a free (noncommutative) group with infinitely many generators is R+ \ {O}. This extends the result of Voiculescu who previously proved [26, 27] that Q+ \ {0} is contained in 9(Y(F )) . This solves a classical problem in the harmonic analysis of the free group F . In particular, it follows that there exists subfactors of _(F7o) with index s for every s E [4, oo) . We will use the noncommutative (quantum… 
Some estimates for the Banach space norms in the von Neumann algebras associated with the Berezin's quantization of compact Riemann
Let $\G$ be any cocompact, discrete subgroup of $\pslr$. In this paper we find estimates for the predual and the uniform Banach space norms in the von Neumann algebras associated with the Berezin' s
Operator algebras, free groups and other groups
The operator algebras associated to non commutative free groups have received a lot of attention, by F.J. Murray and J. von Neumann and by later workers. We review some properties of these algebras,
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 a family of non-almost-periodic free Araki–Woods factors
We obtain a complete classification of a large class of non almost periodic free Araki-Woods factors $\Gamma(\mu,m)"$ up to isomorphism. We do this by showing that free Araki-Woods factors
Compressions of free products of von Neumann algebras
Abstract. A reduction formula for compressions of von Neumann algebra II $_1$–factors arising as free products is proved. This shows that the fundamental group is ${\bf R}^*_+$ for some such
For Free Products of Von Neumann Algebras
Sufficient conditions for factoriality are given for free products of von Neumann algebras with respect to states that are not necessarily traces. The Connes T –invariant of the free product algebra
Free products of finite dimensional and other von Neumann algebras with respect to non-tracial states
The von Neumann algebra free product of arbitary finite dimensional von Neumann algebras with respect to arbitrary faithful states, at least one of which is not a trace, is found to be a type~III
Realization of rigid C$^*$-tensor categories via Tomita bimodules
Starting from a (small) rigid C$^*$-tensor category $\mathscr{C}$ with simple unit, we construct von Neumann algebras associated to each of its objects. These algebras are factors and can be either
Free products of hyperfinite von Neumann algebras and free dimension
The free product of an arbitrary pair of finite hyperfinite von Neumann algebras is examined, and the result is determined to be the direct sum of a finite dimensional algebra and an interpolated
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 50 REFERENCES
Operator Algebras and Applications: Quantized groups, string algebras, and Galois theory for algebras
We introduce a Galois type invariant for the position of a subalgebra inside an algebra, called a paragroup, which has a group-like structure. Paragroups are the natural quantization of (finite)
Conne’s bicentralizer problem and uniqueness of the injective factor of type III1
In Connes' fundamental work "Classification of injective factors" [7], it is proved that injective factors of type III,t, 2 . 1 on a separable Hilbert space are completely classified by their "smooth
Limit laws for Random matrices and free products
In earlier articles we studied a kind of probability theory in the framework of operator algebras, with the tensor product replaced by the free product. We prove here that free random variables
Local observables and particle statistics II
Starting from the principles of local relativistic Quantum Theory without long range forces, we study the structure of the set of superselection sectors (charge quantum numbers) and its implications
Index of subfactors and statistics of quantum fields. I
We identify the statistical dimension of a superselection sector in a local quantum field theory with the square root of the index of a localized endomorphism of the quasi-local C*-algebra that
Duality for crossed products and the structure of von Neumann algebras of type III
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249 Preliminary 251 Construction of crossed products . . . . . . . . . . . . . . . . . . . . . . . 253 Duality . . . . . .
Fundamentals of the Theory of Operator Algebras
On the Distribution of the Roots of Certain Symmetric Matrices
TLDR
The distribution law obtained before' for a very special set of matrices is valid for much more general sets of real symmetric matrices of very high dimensionality.
Une classi cation des facteurs de type III
© Gauthier-Villars (Éditions scientifiques et médicales Elsevier), 1973, tous droits réservés. L’accès aux archives de la revue « Annales scientifiques de l’É.N.S. » (http://www.
Limit laws for random matrices and/ree products, Operator Algebras, Unitary Representations and Invariant Theory, Progress in Math., vol
  • Birkhiiuser,
  • 1990
...
1
2
3
4
5
...