Remote Access Journal of the American Mathematical Society
Green Open Access

Journal of the American Mathematical Society

ISSN 1088-6834(online) ISSN 0894-0347(print)

 
 

 

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: J. Amer. Math. Soc. 5 (1992), 517-532
MSC: Primary 46L10; Secondary 22D25
DOI: https://doi.org/10.1090/S0894-0347-1992-1142260-1
MathSciNet review: 1142260
Full-text PDF Free Access

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • Huzihiro Araki and E. J. Woods, A classification of factors, Publ. Res. Inst. Math. Sci. Ser. A 4 (1968/1969), 51–130. MR 0244773, DOI https://doi.org/10.2977/prims/1195195263
  • M. F. Atiyah and I. M. Singer, The index of elliptic operators. IV, Ann. of Math. (2) 93 (1971), 119–138. MR 279833, DOI https://doi.org/10.2307/1970756
  • A. Connes, A survey of foliations and operator algebras, Operator algebras and applications, Part I (Kingston, Ont., 1980) Proc. Sympos. Pure Math., vol. 38, Amer. Math. Soc., Providence, R.I., 1982, pp. 521–628. MR 679730
  • A. Connes, Classification of injective factors. Cases $II_{1},$ $II_{\infty },$ $III_{\lambda },$ $\lambda \not =1$, Ann. of Math. (2) 104 (1976), no. 1, 73–115. MR 454659, DOI https://doi.org/10.2307/1971057
  • ---, Un facteur du type ${\text {I}}{{\text {I}}_1}$ avec le groupe fondamentale denombrable, J. Operator Theory 4 (1980), 151-153.
  • Alain Connes, Une classification des facteurs de type ${\rm III}$, Ann. Sci. École Norm. Sup. (4) 6 (1973), 133–252 (French). MR 341115
  • A. Connes, Factors of type ${\rm III}_1$, property $L_\lambda ’$ and closure of inner automorphisms, J. Operator Theory 14 (1985), no. 1, 189–211. MR 789385
  • ---, A factor non anti-isomorphic to itself, Ann. of Math. 101 (1974), 536-554. J. Diximier, Les algèbres des operateurs dans l’espaces hilbertien, Gauthier-Villard, Paris, 1969.
  • Sergio Doplicher, Rudolf Haag, and John E. Roberts, Local observables and particle statistics. II, Comm. Math. Phys. 35 (1974), 49–85. MR 334742
  • J. Frolich, Statistics of fields, The Yang Baxter equation and the theory of knots, Proceedings of the 1987 Carése School, World Scientific, London, 1991.
  • Uffe Haagerup, Connes’ bicentralizer problem and uniqueness of the injective factor of type ${\rm III}_1$, Acta Math. 158 (1987), no. 1-2, 95–148. MR 880070, DOI https://doi.org/10.1007/BF02392257
  • V. F. R. Jones, Index for subfactors, Invent. Math. 72 (1983), no. 1, 1–25. MR 696688, DOI https://doi.org/10.1007/BF01389127
  • ---, A polynomial for knots via von Neumann Algebras, Bull. Amer. Math. Soc. 12 (1985), 103-112.
  • Richard V. Kadison and John R. Ringrose, Fundamentals of the theory of operator algebras. Vol. I, Pure and Applied Mathematics, vol. 100, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York, 1983. Elementary theory. MR 719020
  • F. J. Murray and J. von Neumann, On rings of operators. IV, Ann. of Math. (2) 44 (1943), 716–808. MR 9096, DOI https://doi.org/10.2307/1969107
  • A. Ocneanu, Quantized groups, string algebras and Galois theory for algebras, Pitman Lecture Notes, vol. 123, 1990.
  • Sorin Popa, Some rigidity results in type ${\rm II}_1$ factors, C. R. Acad. Sci. Paris Sér. I Math. 311 (1990), no. 9, 535–538 (English, with French summary). MR 1078117
  • S. Popa, Classification of subfactors: the reduction to commuting squares, Invent. Math. 101 (1990), no. 1, 19–43. MR 1055708, DOI https://doi.org/10.1007/BF01231494
  • Robert T. Powers, Representations of uniformly hyperfinite algebras and their associated von Neumann rings, Ann. of Math. (2) 86 (1967), 138–171. MR 218905, DOI https://doi.org/10.2307/1970364
  • Shôichirô Sakai, $C^ *$-algebras and $W^ *$-algebras, Springer-Verlag, New York-Heidelberg, 1971. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 60. MR 0442701
  • I. M. Singer, Some remarks on operator theory and index theory, $K$-theory and operator algebras (Proc. Conf., Univ. Georgia, Athens, Ga., 1975) Springer, Berlin, 1977, pp. 128–138. Lecture Notes in Math., Vol. 575. MR 0467848
  • Ş. Strătilă and L. Zsido, Lectures or von Neumann algebras, Editura Academiei, Bucharest, 1980. M. Takesaki, Theory of operators algebras I, II, Springer, New York, 1979.
  • Masamichi Takesaki, Duality for crossed products and the structure of von Neumann algebras of type III, Acta Math. 131 (1973), 249–310. MR 438149, DOI https://doi.org/10.1007/BF02392041
  • Dan Voiculescu, Limit laws for random matrices and free products, Invent. Math. 104 (1991), no. 1, 201–220. MR 1094052, DOI https://doi.org/10.1007/BF01245072
  • ---, Circular and semicircular systems and free product factors, Inventiones Math. 104 (1991), 201-220.
  • Eugene P. Wigner, On the distribution of the roots of certain symmetric matrices, Ann. of Math. (2) 67 (1958), 325–327. MR 95527, DOI https://doi.org/10.2307/1970008
  • Roberto Longo, Index of subfactors and statistics of quantum fields. I, Comm. Math. Phys. 126 (1989), no. 2, 217–247. MR 1027496

Similar Articles

Retrieve articles in Journal of the American Mathematical Society with MSC: 46L10, 22D25

Retrieve articles in all journals with MSC: 46L10, 22D25


Additional Information

Article copyright: © Copyright 1992 American Mathematical Society