Communications in Mathematical Physics

, Volume 156, Issue 1, pp 17–36 | Cite as

Stable equivalence of the weak closures of free groups convolution algebras

  • Florin Rădulescu


We prove in this paper that the von Neumann algebras associated to the free non-commutative groups are stably isomorphic, i.e. that they are isomorphic when tensorized by the algebra of all linear bounded operators on a separable, infinite dimensional Hilbert space. This gives positive evidence for an old question, due to R.V. Kadison (see also S. Sakai's book on W*-algebras), whether the von Neumann algebras associated to free groups are isomorphic or not.


Neural Network Statistical Physic Free Group Hilbert Space Complex System 
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  1. 1.
    Connes, A.: A survey of foliations and operator algebras. Proc. Symp. Pure Math.38, Part I, 521–628 (1982)Google Scholar
  2. 2.
    Kadison, R.V.: List of open problems at the Baton Rouge Conference. Mimeographed notes 1973Google Scholar
  3. 3.
    Murray, F.J., von Neumann, J.: On rings of Operators. Ann. Math.44, 716–808 (1943)Google Scholar
  4. 4.
    Rădulescu, F.: The fundamental group of ℒ(F is ℝ+∖{0}). J. A.M.S.5, nr. 3, 517–532 (1992)Google Scholar
  5. 5.
    Takesaki, M.: Theory of Operator Algebras, I. II. New York: Springer 1979Google Scholar
  6. 6.
    Voiculescu, D.: Limit laws for random matrices and free products. Invent. Maths.104, 201–220 (1991)CrossRefGoogle Scholar
  7. 7.
    Voiculescu, D.: Circular and semicircular systems and free product factors. In: Operator Algebras, Unitary Representations, Enveloping Algebras. Progress in Math. Vol.92, Basel, Boston: Birkhäuser, pp. 45–60, 1990Google Scholar
  8. 8.
    Dykema, K.: Interpolated group factors. Preprint, U. C. Berkeley, March 1992. To appear in Pacific Journal of MathematicsGoogle Scholar
  9. 9.
    Sakai, S.:C *-Algebras andW *-Algebras. Berlin, Heidelberg, New York: Springer 1971Google Scholar
  10. 10.
    Florin Rădulescu: Random Matrices, Amalgamated free products and subfactors of the von Neumann algebra of a free group. Preprint I.H.E.S. Nr. 89, December 1991Google Scholar

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Florin Rădulescu
    • 1
    • 2
  1. 1.Department of MathematicsU.C.L.A.Los AngelesUSA
  2. 2.I.H.E.S.Bures-sur-YvetteFrance

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