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

  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},
  • 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… 
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Limit laws for random matrices and/ree products, Operator Algebras, Unitary Representations and Invariant Theory, Progress in Math., vol
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