Composition of subfactors : new examples of infinite depth subfactors
Bisch, Dietmar ; Haagerup, Uffe
Annales scientifiques de l'École Normale Supérieure, Tome 29 (1996), p. 329-383 / Harvested from Numdam
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@article{ASENS_1996_4_29_3_329_0,
     author = {Bisch, Dietmar and Haagerup, Uffe},
     title = {Composition of subfactors : new examples of infinite depth subfactors},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {29},
     year = {1996},
     pages = {329-383},
     doi = {10.24033/asens.1742},
     mrnumber = {97e:46080},
     zbl = {0853.46062},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ASENS_1996_4_29_3_329_0}
}

Bisch, Dietmar; Haagerup, Uffe. Composition of subfactors : new examples of infinite depth subfactors. Annales scientifiques de l'École Normale Supérieure, Tome 29 (1996) pp. 329-383. doi : 10.24033/asens.1742. http://gdmltest.u-ga.fr/item/ASENS_1996_4_29_3_329_0/

[ABH] J. Anderson, B. Blackadar and U. Haagerup, Minimal projections in the reduced groups C*-algebra of ℤn * ℤM, (J. of Operator Theory, Vol. 26, 1991, pp. 3-23). | MR 1214917 | MR 94c:46110 | Zbl 0785.46050

[Av] Avez, Entropy des groupes de type fini (C. R. Acad. Sci. Paris, Vol. 275A, 1972, pp. 1363-1366). | MR 324741 | MR 48 #3090 | Zbl 0252.94013

[BC] Ch. Berg and J. P. R. Christensen, Sur la norme des opérateurs de convolution (Invent. math., Vol. 23, 1974, pp. 173-178). | MR 338685 | MR 49 #3449 | Zbl 0261.22009 | Zbl 0267.22007

[Bi1] D. Bisch, Entropy of groups and subfactors (Journal of Funct. Analysis, Vol. 103, 1992, pp. 190-208). | MR 1144689 | MR 93e:46076 | Zbl 0829.46050

[Bi2] D. Bisch, A note on intermediate subfactors (Pacific Journal of Math., Vol. 163, 1994, pp. 201-216). | MR 1262294 | MR 95c:46105 | Zbl 0814.46053

[Bi3] D. Bisch, On the structure of finite depth subfactors (in Algebraic Methods in Operator Theory, Birkhäuser, 1994, pp. 175-194). | MR 1284945 | MR 95j:46073 | Zbl 0809.46069

[Bu] W. Burnside, Theory of groups of finite order, Cambridge University Press, 1911. | JFM 42.0151.02

[CD] G. Choquet, J. Deny, Sur l'équation de convolution µ = µ * σ (C. R. Acad. Sci. Paris, Vol. 250A, 1960, pp. 799-801). | MR 119041 | MR 22 #9808 | Zbl 0093.12802

[Co] A. Connes, Notes on correspondences, unpublished manuscript.

[CM] H. S. M. Coxeter and W. O. J. Moser, Generators and relations for discrete groups (Springer-Verlag, New York, Berlin, Heidelberg, 2nd edition, 1972). | MR 50 #2313 | Zbl 0239.20040

[DG] Y. Derriennic and Y. Guivarc'H, Théorème de renouvellement pour les groups non-moyennables (C. R. Acad. Sci. Paris, Série A, Vol. 277, 1973, pp. 613-615). | MR 48 #7332 | Zbl 0272.60005

[Fu] H. Furstenberg, Random walks and discrete subgroups of Lie groups (in Adv. Prob. Related Topics, Dekker, New York, Vol. 1, 1971, pp. 1-63). | MR 44 #1794 | Zbl 0221.22008

[GHJ] F. Goodman, P. De La Harpe, and V. Jones, Coxeter graphs and towers of algebras, Springer-Verlag, MSRI publications, 1989. | MR 91c:46082 | Zbl 0698.46050

[G] F. P. Greenleaf, Invariant means on topological groups and their applications, Van Nostrand, New York, 1969. | MR 40 #4776 | Zbl 0174.19001

[Ha] U. Haagerup, Principal graphs of subfactors in the index range 4 < [M : N] < 3 + √2 (in ”Subfactors”, Proceedings of the Taniguchi Symposium on Operator Algebras, 1994, pp. 1-38). | MR 96d:46081 | Zbl 0933.46058

[Hi] F. Hiai, Entropy and growth for derived towers of subfactors (in “Subfactors”, Proceedings of the Taniguchi Symposium on Operator Algebras, 1994, pp. 206-232). | MR 96c:46060 | Zbl 0932.46049

[HPS] G. Hole, S. C. Port and C. J. Stone, Introduction to stochastical processes, Houghton Mifflin Co., 1972. | Zbl 0258.60003

[Jo] V. F. R. Jones, Index for subfactors (Invent. Math., Vol. 72, 1983, pp. 1-25). | MR 84d:46097 | Zbl 0508.46040

[KV] V. A. Kaimanovich and A. M. Vershik, Random walks on discrete groups : Boundary and entropy (Ann. Probab., Vol. 11, No. 3, 1983, pp. 457-490). | MR 85d:60024 | Zbl 0641.60009

[Ka1] V. A. Kaimanovich, Poisson boundaries of random walks on discrete solvable groups (Proc. 10th Oberwolfach Conf. on Prob. Measures on groups, ed. H. Heyer, Plenum, New York, 1991, pp. 205-238). | MR 94m:60014 | Zbl 0823.60006

[Ka2] V. A. Kaimanovich, The Poisson boundary of covering Markov operators, to appear in Israel Journal of Math. | Zbl 0843.43001

[Ka3] V. A. Kaimanovich, Bi-harmonic functions on groups (C. R. Acad. Sci. Paris, Vol. 314, 1992, pp. 259-262). | MR 93e:60160 | Zbl 0754.60015

[Ka4] V. A. Kaimanovich, Examples of non-commutative groups with non-trivial exit boundary (J. Soviet Math., Vol. 28, 1985, pp. 579-591). | Zbl 0558.60010

[Ke] H. Kesten, Symmetric random walks on groups (Trans. Amer. Math. Soc., Vol. 92, 1959, pp. 336-354). | MR 22 #253 | Zbl 0092.33503

[K] A. W. Knapp, Doubly generated Fuchsian groups (Michigan Math. Journal, Vol. 15, 1968, pp. 289-304). | MR 40 #1483 | Zbl 0167.07002

[M] J. P. Matelski, The classification of discrete 2-generator subgroups of PSL(2, ℝ) (Israel J. Math., Vol. 42, 1982, pp. 309-317). | MR 84d:10029 | Zbl 0497.20036

[Me] J. L. Mennicke, Finite factor groups of the unimodular group (Ann. of Math., Vol. 81, 1965, pp. 31-37). | MR 30 #2083 | Zbl 0135.06504

[Ne] M. Newman, The structure of some subgroups of the modular group (Ill. Jour. of Math., Vol. 6, 1962, pp. 480-487). | MR 25 #4001 | Zbl 0104.25301

[Oc1] A. Ocneanu, Quantized group string algebras and Galois theory for operator algebras, in Operator Algebras and Applications 2 (London Math. Soc. Lect., Notes Series, Vol. 136, 1988, pp. 119-172). | MR 91k:46068 | Zbl 0696.46048

[Oc2] A. Ocneanu, Quantum symmetry, differential geometry of finite graphs and classification of subfactors University of Tokyo Seminary Notes (notes recorded by Y. Kawahigashi), Vol. 45, 1991.

[Po1] S. Popa, Correspondences, Increst preprint, 1986.

[Po2] S. Popa, Classification of subfactors : reduction to commuting squares (Invent. Math., Vol. 101, 1990, pp. 19-43). | MR 91h:46109 | Zbl 0757.46054

[Po3] S. Popa, Sous-facteurs, actions des groupes et cohomologie (C. R. Acad. Sci. Paris, Vol. 309, 1989, pp. 771-776). | MR 91i:46069 | Zbl 0684.46051

[Po4] S. Popa, Classification of amenable subfactors of type II (Acta Math., Vol. 172, 1994, pp. 352-445). | MR 95f:46105 | Zbl 0853.46059

[Po5] S. Popa, Symmetric enveloping algebras, amenability and AFD properties for subfactors (Mathematical Research Letters, Vol. 1, 1994, pp. 409-425). | MR 95i:46095 | Zbl 0902.46042

[Po6] S. Popa, Approximate innerness and central freeness for subfactors : A classification result, preprint 1993.

[R] G. Rosenberger, All generating pairs of all two-generator Fuchsian groups (Arch. Math., Vol 46, 1986, pp. 198-204). | MR 87g:20080 | Zbl 0563.20043

[Se] E. Seneta, Non-negative matrices and Markov chains, Springer Verlag, 1981. | MR 85i:60058 | Zbl 0471.60001

[Sp] F. Spitzer, Principles of Random walks, 2nd ed. Springer Verlag, New York, Heidelberg, Berlin, 1976. | MR 52 #9383 | Zbl 0359.60003

[Su] V. S. Sunder, II1 factors, their bimodules and hypergroups (Trans. Amer. Math. Soc., Vol. 330, 1992, pp. 227-256). | MR 92f:46076 | Zbl 0757.46053

[Sz] W. Szymanski, Finite index subfactors and Hopf algebra crossed products (Proc. of the Amer. Math. Soc, Vol. 120, 1994, pp. 519-528). | MR 94d:46061 | Zbl 0802.46076

[Voi] D. Voiculescu, Symmetries of some reduced free product C*-algebras (in Operator Algebras and Their Connections with Topology and Ergodic Theory, Lecture Notes in Mathematics, Springer Verlag, Vol. 1132, 1985, pp. 556-588). | MR 87d:46075 | Zbl 0618.46048

[Wi] J. Wierzbicki, The estimation of the depth from an intermediate subfactor, preprint 1993.

[Wo] W. Woess, Random walks on infinite graphs and groups - a survey on selected topics (Bull. London Math. Soc., Vol. 26, 1994, pp. 1-60). | MR 94i:60081 | Zbl 0830.60061

[Ya] S. Yamagami, A note on Ocneanu's approach to Jones' index theory (Internat. J. of Math., Vol. 4, 1993, pp. 859-871). | MR 95f:46114 | Zbl 0793.46040