Duke Mathematical Journal

Free products of hyperfinite von Neumann algebras and free dimension

Ken Dykema

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Article information

Duke Math. J. Volume 69, Number 1 (1993), 97-119.

First available in Project Euclid: 20 February 2004

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46L35: Classifications of $C^*$-algebras


Dykema, Ken. Free products of hyperfinite von Neumann algebras and free dimension. Duke Math. J. 69 (1993), no. 1, 97--119. doi:10.1215/S0012-7094-93-06905-0. http://projecteuclid.org/euclid.dmj/1077293426.

Export citation


  • [1'] F. Boca, On the method of constructing irreducible finite-index subfactors of Popa, Preprint, U.C.L.A., December 1991.
  • [1] W. M. Ching, Free products of von Neumann algebras, Trans. Amer. Math. Soc. 178 (1973), 147–163.
  • [2] A. Connes, Classification of injective factors. Cases $II\sb1,$ $II\sb\infty ,$ $III\sb\lambda ,$ $\lambda \not=1$, Ann. of Math. (2) 104 (1976), no. 1, 73–115.
  • [3] K. Dykema, On certain free-product factors via an extended matrix model, to appear in J. Funct. Anal.
  • [4] K. Dykema, Interpolated free group factors, to appear in Pacific J. Math.
  • [5] F. J. Murray and J. von Neumann, On Rings of operators. IV, Ann. of Math. (2) 44 (1943), 716–808.
  • [6] S. Popa, Markov traces on universal Jones algebras and subfactors of finite index, preprint, I.H.E.S., June 1991.
  • [7] F. Rădulescu, The fundamental group of the von Neumann algebra of a free group with infinitely many generators is $\mathbfR_+\0\$, to appear in J. Amer. Math. Soc.
  • [8] F. Rădulescu, Stable isomorphism of the weak closure of free group convolution algebras, preprint, I.H.E.S., December 1991.
  • [9] F. Rădulescu, Random matrices, amalgamated free products, and subfactors of the von Neumann algebra of a free group, preprint, I.H.E.S., December 1991.
  • [10] D. Voiculescu, Symmetries of some reduced free product $C\sp \ast$-algebras, Operator algebras and their connections with topology and ergodic theory (Buşteni, 1983), Lecture Notes in Math., vol. 1132, Springer, Berlin, 1985, pp. 556–588.
  • [11] D. Voiculescu, Multiplication of certain noncommuting random variables, J. Operator Theory 18 (1987), no. 2, 223–235.
  • [12] D. Voiculescu, Noncommutative random variables and spectral problems in free product $C\sp *$-algebras, Rocky Mountain J. Math. 20 (1990), no. 2, 263–283.
  • [13] D. Voiculescu, Circular and semicircular systems and free product factors, Operator Algebras, Unitary Representations, Enveloping Algebras, and Invariant Theory (Paris, 1989), Progr. Math., vol. 92, Birkhäuser, Boston, 1990, pp. 45–60.
  • [14] D. Voiculescu, Limit laws for random matrices and free products, Invent. Math. 104 (1991), no. 1, 201–220.
  • [15] D. Voiculescu, Free noncommutative random variables, random matrices and the $\rm II\sb 1$ factors of free groups, Quantum probability & related topics, QP-PQ, VI, World Sci. Publishing, River Edge, NJ, 1991, pp. 473–487.