Conjugate but non inner conjugate subfactors
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- Proc. Amer. Math. Soc. 124 (1996), 147-153 Request permission
Abstract:
It is shown that for each $r \in \{4\cos ^{2}(\pi /n): n \ge 3\} \cup [4, \infty ),$ there exist at least infinitely many subfactors of the hyperfinite II$_{1}$ factor $R$ with index $r,$ which are pairwise conjugate but non inner conjugate. In the case that $r$ is an integer, we have uncountably many such subfactors of $R.$References
- Jocelyne Bion-Nadal, An example of a subfactor of the hyperfinite $\textrm {II}_1$ factor whose principal graph invariant is the Coxeter graph $E_6$, Current topics in operator algebras (Nara, 1990) World Sci. Publ., River Edge, NJ, 1991, pp. 104–113. MR 1193933
- Marie Choda, Entropy for canonical shifts, Trans. Amer. Math. Soc. 334 (1992), no. 2, 827–849. MR 1070349, DOI 10.1090/S0002-9947-1992-1070349-0
- A. Connes, Outer conjugacy of automorphisms of factors, Symposia Mathematica, Vol. XX (Convegno sulle Algebre $C^*$ e loro Applicazioni in Fisica Teorica, Convegno sulla Teoria degli Operatori Indice e Teoria $K$, INDAM, Rome, 1975) Academic Press, London, 1976, pp. 149–159. MR 0450987
- A. Connes, Periodic automorphisms of the hyperfinite factor of type II1, Acta Sci. Math. (Szeged) 39 (1977), no. 1-2, 39–66. MR 448101
- Frederick M. Goodman, Pierre de la Harpe, and Vaughan F. R. Jones, Coxeter graphs and towers of algebras, Mathematical Sciences Research Institute Publications, vol. 14, Springer-Verlag, New York, 1989. MR 999799, DOI 10.1007/978-1-4613-9641-3
- Masaki Izumi, Application of fusion rules to classification of subfactors, Publ. Res. Inst. Math. Sci. 27 (1991), no. 6, 953–994. MR 1145672, DOI 10.2977/prims/1195169007
- —, On flatness of the Coxeter graph $E_{8}$, Pacific J. Math. (to appear).
- Masaki Izumi and Yasuyuki Kawahigashi, Classification of subfactors with the principal graph $D^{(1)}_n$, J. Funct. Anal. 112 (1993), no. 2, 257–286. MR 1213139, DOI 10.1006/jfan.1993.1033
- Vaughan F. R. Jones, Actions of finite groups on the hyperfinite type $\textrm {II}_{1}$ factor, Mem. Amer. Math. Soc. 28 (1980), no. 237, v+70. MR 587749, DOI 10.1090/memo/0237
- V. F. R. Jones, Index for subfactors, Invent. Math. 72 (1983), no. 1, 1–25. MR 696688, DOI 10.1007/BF01389127
- Y. Kawahigashi, On flatness of Ocneanu’s connections on the Dynkin diagrams and classification of subfactors, J. Funct. Anal. 127 (1995), 63–107.
- Hideki Kosaki and Shigeru Yamagami, Irreducible bimodules associated with crossed product algebras, Internat. J. Math. 3 (1992), no. 5, 661–676. MR 1189679, DOI 10.1142/S0129167X9200031X
- Adrian Ocneanu, Quantized groups, string algebras and Galois theory for algebras, Operator algebras and applications, Vol. 2, London Math. Soc. Lecture Note Ser., vol. 136, Cambridge Univ. Press, Cambridge, 1988, pp. 119–172. MR 996454
- —, Quantum symmetry, differential geometry of finite graphs and classification of subfactors, University of Tokyo Seminary Notes 45 (notes recorded by Y. Kawahigashi), 1991.
- Mihai Pimsner and Sorin Popa, Entropy and index for subfactors, Ann. Sci. École Norm. Sup. (4) 19 (1986), no. 1, 57–106. MR 860811, DOI 10.24033/asens.1504
- S. Popa, Classification of subfactors: the reduction to commuting squares, Invent. Math. 101 (1990), no. 1, 19–43. MR 1055708, DOI 10.1007/BF01231494
- Sorin Popa, Sur la classification des sous-facteurs d’indice fini du facteur hyperfini, C. R. Acad. Sci. Paris Sér. I Math. 311 (1990), no. 2, 95–100 (French, with English summary). MR 1065437
- Sorin Popa, Classification of amenable subfactors of type II, Acta Math. 172 (1994), no. 2, 163–255. MR 1278111, DOI 10.1007/BF02392646
- V. S. Sunder and A. K. Vijayarajan, On the nonoccurrence of the Coxeter graphs $\beta _{2n+1},\ D_{2n+1}$ and $E_7$ as the principal graph of an inclusion of $\textrm {II}_1$ factors, Pacific J. Math. 161 (1993), no. 1, 185–200. MR 1237144, DOI 10.2140/pjm.1993.161.185
- Antony Wassermann, Coactions and Yang-Baxter equations for ergodic actions and subfactors, Operator algebras and applications, Vol. 2, London Math. Soc. Lecture Note Ser., vol. 136, Cambridge Univ. Press, Cambridge, 1988, pp. 203–236. MR 996457
- Hans Wenzl, Hecke algebras of type $A_n$ and subfactors, Invent. Math. 92 (1988), no. 2, 349–383. MR 936086, DOI 10.1007/BF01404457
Additional Information
- Marie Choda
- Affiliation: Department of Mathematics, Osaka Kyoiku University, Asahigaoka, Kashiwara 582, Japan
- Email: foo527@sinet.ad.jp
- Received by editor(s): April 4, 1994
- Received by editor(s) in revised form: July 7, 1994
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 147-153
- MSC (1991): Primary 46L37; Secondary 46L40
- DOI: https://doi.org/10.1090/S0002-9939-96-02997-8
- MathSciNet review: 1285982