Skip to Main Content

Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

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

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

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

by Florin Rădulescu
J. Amer. Math. Soc. 5 (1992), 517-532
DOI: https://doi.org/10.1090/S0894-0347-1992-1142260-1
References
  • 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 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 10.2307/1970756
  • A. Connes, A survey of foliations and operator algebras, Operator algebras and applications, Part 1 (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 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 $\textrm {III}$, Ann. Sci. École Norm. Sup. (4) 6 (1973), 133–252 (French). MR 341115, DOI 10.24033/asens.1247
  • A. Connes, Factors of type $\textrm {III}_1$, 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, DOI 10.1007/BF01646454
  • 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 $\textrm {III}_1$, Acta Math. 158 (1987), no. 1-2, 95–148. MR 880070, DOI 10.1007/BF02392257
  • V. F. R. Jones, Index for subfactors, Invent. Math. 72 (1983), no. 1, 1–25. MR 696688, DOI 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 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 $\textrm {II}_1$ 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 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 10.2307/1970364
  • Shôichirô Sakai, $C^*$-algebras and $W^*$-algebras, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 60, Springer-Verlag, New York-Heidelberg, 1971. 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) Lecture Notes in Math., Vol. 575, Springer, Berlin, 1977, pp. 128–138. 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 10.1007/BF02392041
  • Dan Voiculescu, Limit laws for random matrices and free products, Invent. Math. 104 (1991), no. 1, 201–220. MR 1094052, DOI 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 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, DOI 10.1007/BF02125124
Similar Articles
  • Retrieve articles in Journal of the American Mathematical Society with MSC: 46L10, 22D25
  • Retrieve articles in all journals with MSC: 46L10, 22D25
Bibliographic Information
  • © Copyright 1992 American Mathematical Society
  • 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