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

Rădulescu, Florin

doi:10.1090/S0894-0347-1992-1142260-1

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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
MathSciNet review: 1142260
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[1] Huzihiro Araki and E. J. Woods, A classification of factors, Publ. Res. Inst. Math. Sci. Ser. A 4 (1968/1969), 51–130. MR 0244773 (39 #6087)
[2] M. F. Atiyah and I. M. Singer, The index of elliptic operators. IV, Ann. of Math. (2) 93 (1971), 119–138. MR 0279833 (43 #5554)
[3] 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 (84m:58140)
[4] A. Connes, Classification of injective factors. Cases 𝐼𝐼₁, 𝐼𝐼_{∞}, 𝐼𝐼𝐼_{𝜆}, 𝜆̸=1, Ann. of Math. (2) 104 (1976), no. 1, 73–115. MR 0454659 (56 #12908)
[5] -, Un facteur du type ${\text{I}}{{\text{I}}_1}$ avec le groupe fondamentale denombrable, J. Operator Theory 4 (1980), 151-153.
[6] Alain Connes, Une classification des facteurs de type 𝐼𝐼𝐼, Ann. Sci. École Norm. Sup. (4) 6 (1973), 133–252 (French). MR 0341115 (49 #5865)
[7] A. Connes, Factors of type 𝐼𝐼𝐼₁, property 𝐿_{𝜆}’ and closure of inner automorphisms, J. Operator Theory 14 (1985), no. 1, 189–211. MR 789385 (88b:46088)
[8] -, A factor non anti-isomorphic to itself, Ann. of Math. 101 (1974), 536-554.
[9] J. Diximier, Les algèbres des operateurs dans l'espaces hilbertien, Gauthier-Villard, Paris, 1969.
[10] Sergio Doplicher, Rudolf Haag, and John E. Roberts, Local observables and particle statistics. II, Comm. Math. Phys. 35 (1974), 49–85. MR 0334742 (48 #13060)
[11] J. Frolich, Statistics of fields, The Yang Baxter equation and the theory of knots, Proceedings of the 1987 Carése School, World Scientific, London, 1991.
[12] Uffe Haagerup, Connes’ bicentralizer problem and uniqueness of the injective factor of type 𝐼𝐼𝐼₁, Acta Math. 158 (1987), no. 1-2, 95–148. MR 880070 (88f:46117), http://dx.doi.org/10.1007/BF02392257
[13] V. F. R. Jones, Index for subfactors, Invent. Math. 72 (1983), no. 1, 1–25. MR 696688 (84d:46097), http://dx.doi.org/10.1007/BF01389127
[14] -, A polynomial for knots via von Neumann Algebras, Bull. Amer. Math. Soc. 12 (1985), 103-112.
[15] 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 (85j:46099)
[16] F. J. Murray and J. von Neumann, On rings of operators. IV, Ann. of Math. (2) 44 (1943), 716–808. MR 0009096 (5,101a)
[17] A. Ocneanu, Quantized groups, string algebras and Galois theory for algebras, Pitman Lecture Notes, vol. 123, 1990.
[18] Sorin Popa, Some rigidity results in type 𝐼𝐼₁ factors, C. R. Acad. Sci. Paris Sér. I Math. 311 (1990), no. 9, 535–538 (English, with French summary). MR 1078117 (92e:46123)
[19] S. Popa, Classification of subfactors: the reduction to commuting squares, Invent. Math. 101 (1990), no. 1, 19–43. MR 1055708 (91h:46109), http://dx.doi.org/10.1007/BF01231494
[20] Robert T. Powers, Representations of uniformly hyperfinite algebras and their associated von Neumann rings, Ann. of Math. (2) 86 (1967), 138–171. MR 0218905 (36 #1989)
[21] Shôichirô Sakai, 𝐶*-algebras and 𝑊*-algebras, Springer-Verlag, New York, 1971. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 60. MR 0442701 (56 #1082)
[22] 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 (57 #7699)
[23] Ş. Strătilă and L. Zsido, Lectures or von Neumann algebras, Editura Academiei, Bucharest, 1980.
[24] M. Takesaki, Theory of operators algebras I, II, Springer, New York, 1979.
[25] Masamichi Takesaki, Duality for crossed products and the structure of von Neumann algebras of type III, Acta Math. 131 (1973), 249–310. MR 0438149 (55 #11068)
[26] Dan Voiculescu, Limit laws for random matrices and free products, Invent. Math. 104 (1991), no. 1, 201–220. MR 1094052 (92d:46163), http://dx.doi.org/10.1007/BF01245072
[27] -, Circular and semicircular systems and free product factors, Inventiones Math. 104 (1991), 201-220.
[28] Eugene P. Wigner, On the distribution of the roots of certain symmetric matrices, Ann. of Math. (2) 67 (1958), 325–327. MR 0095527 (20 #2029)
[29] Roberto Longo, Index of subfactors and statistics of quantum fields. I, Comm. Math. Phys. 126 (1989), no. 2, 217–247. MR 1027496 (91c:46097)

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