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Volumn 9, Issue 3, 1998, Pages 669-722

Amenability and strong amenability for fusion algebras with applications to subfactor theory

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EID: 0032329429     PISSN: 0129167X     EISSN: None     Source Type: Journal    
DOI: 10.1142/s0129167x98000300     Document Type: Article
Times cited : (46)

References (79)
  • 1
    • 0000566360 scopus 로고
    • Entropie des groupes de type fini
    • 1. A. Avez, Entropie des groupes de type fini, C. R. Acad. Sci. Paris Sér. A 275 (1972), 1363-1366.
    • (1972) C. R. Acad. Sci. Paris Sér. A , vol.275 , pp. 1363-1366
    • Avez, A.1
  • 2
    • 0000215856 scopus 로고
    • Limite de quotients pour des marches aléatoires sur des groupes
    • 2. A. Avez, Limite de quotients pour des marches aléatoires sur des groupes, C. R. Acad. Sci. Paris Sér. A 276 (1973), 317-320.
    • (1973) C. R. Acad. Sci. Paris Sér. A , vol.276 , pp. 317-320
    • Avez, A.1
  • 3
    • 0009979371 scopus 로고
    • Sur la norme des opérateurs de convolution
    • 3. C. Berg and J. P. R. Christensen, Sur la norme des opérateurs de convolution, Invent. Math. 23 (1974), 173-178.
    • (1974) Invent. Math. , vol.23 , pp. 173-178
    • Berg, C.1    Christensen, J.P.R.2
  • 5
    • 38249014647 scopus 로고
    • Entropy of groups and subfactors
    • 5. D. Bisch, Entropy of groups and subfactors, J. Funct. Anal. 103 (1992), 190-208.
    • (1992) J. Funct. Anal. , vol.103 , pp. 190-208
    • Bisch, D.1
  • 6
    • 0001735230 scopus 로고
    • A note on intermediate subfactors
    • 6. D. Bisch, A note on intermediate subfactors, Pacific J. Math. 163 (1994), 201-216.
    • (1994) Pacific J. Math. , vol.163 , pp. 201-216
    • Bisch, D.1
  • 7
    • 0038701519 scopus 로고    scopus 로고
    • Bimodules, higher relative commutants and the fusion algebra associated to a subfactor
    • P. A. Fillmore and J. A. Mingo, Fields Institute Communications, Amer. Math. Soc., Providence, RI
    • 7. D. Bisch, Bimodules, higher relative commutants and the fusion algebra associated to a subfactor, in Operator Algebras and Their Applications, eds. P. A. Fillmore and J. A. Mingo, Fields Institute Communications, Vol. 13, Amer. Math. Soc., Providence, RI, 1997, pp. 16-63.
    • (1997) Operator Algebras and Their Applications , vol.13 , pp. 16-63
    • Bisch, D.1
  • 8
    • 0000959468 scopus 로고    scopus 로고
    • Composition of subfactors: New examples of infinite depth subfactors
    • 8. D. Bisch and U. Haagerup, Composition of subfactors: new examples of infinite depth subfactors, Ann. Sci. École Norm. Sup. Sér. 4, 29 (1996), 329-383.
    • (1996) Ann. Sci. École Norm. Sup. Sér. 4 , vol.29 , pp. 329-383
    • Bisch, D.1    Haagerup, U.2
  • 9
    • 0031503616 scopus 로고    scopus 로고
    • Algebras associated to intermediate subfactors
    • 9. D. Bisch and V. Jones, Algebras associated to intermediate subfactors, Invent. Math. 128 (1997), 89-157.
    • (1997) Invent. Math. , vol.128 , pp. 89-157
    • Bisch, D.1    Jones, V.2
  • 12
    • 0000722345 scopus 로고
    • A transmutation formula for Markov chains
    • 12. T. K. Carne, A transmutation formula for Markov chains, Bull. Sci. Math. 109 (2) (1985), 399-405.
    • (1985) Bull. Sci. Math. , vol.109 , Issue.2 , pp. 399-405
    • Carne, T.K.1
  • 13
    • 0001636023 scopus 로고
    • Entropy for *-endomorphisms and relative entropy for subalgebras
    • 13. M. Choda, Entropy for *-endomorphisms and relative entropy for subalgebras, J. Operator Theory 25 (1991), 125-140.
    • (1991) J. Operator Theory , vol.25 , pp. 125-140
    • Choda, M.1
  • 14
    • 0001522903 scopus 로고
    • Entropy for canonical shifts
    • 14. M. Choda, Entropy for canonical shifts, Trans. Amer. Math. Soc. 334 (1992), 827-849.
    • (1992) Trans. Amer. Math. Soc. , vol.334 , pp. 827-849
    • Choda, M.1
  • 15
    • 85007966761 scopus 로고
    • Entropy for canonical shifts. II
    • 15. M. Choda and F. Hiai, Entropy for canonical shifts. II, Publ. Res. Inst. Math. Sci. 27 (1991), 461-489.
    • (1991) Publ. Res. Inst. Math. Sci. , vol.27 , pp. 461-489
    • Choda, M.1    Hiai, F.2
  • 16
    • 0010049714 scopus 로고    scopus 로고
    • Notes on correspondences, unpublished manuscript
    • 16. A. Connes, Notes on correspondences, unpublished manuscript.
    • Connes, A.1
  • 17
    • 0000078088 scopus 로고
    • Théorème de renouvellement pour les groupes non moyennables
    • 17. Y. Derriennic and Y. Guivarc'h, Théorème de renouvellement pour les groupes non moyennables, C. R. Acad. Sci. Paris Sér. A 277 (1973), 613-615.
    • (1973) C. R. Acad. Sci. Paris Sér. A , vol.277 , pp. 613-615
    • Derriennic, Y.1    Guivarc'h, Y.2
  • 18
    • 0001078055 scopus 로고
    • Iterates of a convolution on a non abelian group
    • 18. S. R. Foguel, Iterates of a convolution on a non abelian group, Ann. Inst. H. Poincaré Probab. Statist. 11 (1975), 199-202.
    • (1975) Ann. Inst. H. Poincaré Probab. Statist. , vol.11 , pp. 199-202
    • Foguel, S.R.1
  • 19
    • 0009977451 scopus 로고
    • Remarks on amenability of discrete hypergroups
    • M. A. Picardello, Plenum Press, New York
    • 19. M. O. Gebuhrer, Remarks on amenability of discrete hypergroups, in Harmonic Analysis and Discrete Potential Theory, ed. M. A. Picardello, Plenum Press, New York, 1992, pp. 131-143.
    • (1992) Harmonic Analysis and Discrete Potential Theory , pp. 131-143
    • Gebuhrer, M.O.1
  • 20
    • 0000292564 scopus 로고
    • Random walks on graphs with a strong isoperimetnc property
    • 20. P. Gerl, Random walks on graphs with a strong isoperimetnc property, J. Theoret. Probab. 1 (1988), 171-187.
    • (1988) J. Theoret. Probab. , vol.1 , pp. 171-187
    • Gerl, P.1
  • 25
    • 0000639992 scopus 로고
    • Equivalence of normal states on von Neumann algebras and the flow of weights
    • 25. U. Haagerup and E. Størmer, Equivalence of normal states on von Neumann algebras and the flow of weights, Adv. Math. 83 (1990), 180-262.
    • (1990) Adv. Math. , vol.83 , pp. 180-262
    • Haagerup, U.1    Størmer, E.2
  • 26
    • 0000395870 scopus 로고
    • Pointwise inner automorphisms of von Neumann algebras
    • 26. U. Haagerup and E. Størmer, Pointwise inner automorphisms of von Neumann algebras, J. Funct. Anal. 92 (1990), 177-201.
    • (1990) J. Funct. Anal. , vol.92 , pp. 177-201
    • Haagerup, U.1    Størmer, E.2
  • 27
    • 0000097508 scopus 로고
    • Pointwise inner automorphisms of injective factors
    • 27. U. Haagerup and E. Størmer, Pointwise inner automorphisms of injective factors, J. Funct. Anal. 122 (1994), 307-314.
    • (1994) J. Funct. Anal. , vol.122 , pp. 307-314
    • Haagerup, U.1    Størmer, E.2
  • 28
    • 0002514722 scopus 로고
    • Representation rings as invariants for compact groups and limit ratio theorems for them
    • 28. D. Handelman, Representation rings as invariants for compact groups and limit ratio theorems for them, Int. J. Math. 4 (1993), 59-88.
    • (1993) Int. J. Math. , vol.4 , pp. 59-88
    • Handelman, D.1
  • 30
    • 85007996108 scopus 로고
    • Minimizing indices of conditional expectations onto a subfactor
    • 30. F. Hiai, Minimizing indices of conditional expectations onto a subfactor. Publ. Res. Inst. Math. Sci. 24 (1988), 673-678.
    • (1988) Publ. Res. Inst. Math. Sci. , vol.24 , pp. 673-678
    • Hiai, F.1
  • 31
    • 0002886798 scopus 로고
    • Entropy and growth for derived towers of subfactors
    • H. Araki et al., World Scientific, Singapore
    • 31. F. Hiai, Entropy and growth for derived towers of subfactors, in Subfactors, eds. H. Araki et al., World Scientific, Singapore, 1994, pp. 206-232.
    • (1994) Subfactors , pp. 206-232
    • Hiai, F.1
  • 32
    • 0001481950 scopus 로고
    • Entropy for canonical shifts and strong amenability
    • 32. F. Hiai, Entropy for canonical shifts and strong amenability, Int. J. Math. 6 (1995), 381-396.
    • (1995) Int. J. Math. , vol.6 , pp. 381-396
    • Hiai, F.1
  • 33
    • 0009979664 scopus 로고    scopus 로고
    • Standard invariants for crossed product inclusions of factors
    • 33. F. Hiai, Standard invariants for crossed product inclusions of factors, Pacific J. Math. 177 (1997), 237-267.
    • (1997) Pacific J. Math. , vol.177 , pp. 237-267
    • Hiai, F.1
  • 34
    • 85007973526 scopus 로고
    • Application of fusion rules to classification of subfactors
    • 34. M. Izumi, Application of fusion rules to classification of subfactors, Publ. Res. Inst. Math. Sci. 27 (1991), 953-994.
    • (1991) Publ. Res. Inst. Math. Sci. , vol.27 , pp. 953-994
    • Izumi, M.1
  • 35
    • 1842426078 scopus 로고
    • On type II and type III principal graphs of subfactors
    • 35. M. Izumi, On type II and type III principal graphs of subfactors, Math. Scand. 73 (1993), 307-319.
    • (1993) Math. Scand. , vol.73 , pp. 307-319
    • Izumi, M.1
  • 36
    • 0000322219 scopus 로고
    • Canonical extension of endomorphisms on factors
    • H. Araki et al. World Scientific, Singapore
    • 36. M. Izumi, Canonical extension of endomorphisms on factors, in Subfactors, eds. H. Araki et al. World Scientific, Singapore, 1994, pp. 129-138.
    • (1994) Subfactors , pp. 129-138
    • Izumi, M.1
  • 37
    • 0010806038 scopus 로고
    • Index for subfactors
    • 37. V. F. R. Jones, Index for subfactors. Invent. Math. 72 (1983), 1-25.
    • (1983) Invent. Math. , vol.72 , pp. 1-25
    • Jones, V.F.R.1
  • 38
    • 0001414233 scopus 로고
    • Measure-theoretic boundaries of Markov chains, 0-2 laws and entropy
    • M. A. Picardello, Plenum Press, New York
    • 38. V. A. Kaimanovich, Measure-theoretic boundaries of Markov chains, 0-2 laws and entropy, in Harmonic Analysis and Discrete Potential Theory, ed. M. A. Picardello, Plenum Press, New York, 1992, pp. 145-180.
    • (1992) Harmonic Analysis and Discrete Potential Theory , pp. 145-180
    • Kaimanovich, V.A.1
  • 39
    • 51249169054 scopus 로고
    • The Poisson boundary of covering Markov operators
    • 39. V. Kaimanovich, The Poisson boundary of covering Markov operators, Israel J. Math. 89 (1995), 77-134.
    • (1995) Israel J. Math. , vol.89 , pp. 77-134
    • Kaimanovich, V.1
  • 40
    • 0000220740 scopus 로고
    • Random walks on discrete groups: Boundary and entropy
    • 40. V. A. Kaimanovich and A. M. Vershik, Random walks on discrete groups: boundary and entropy, Ann. Probab. 11 (1983), 457-490.
    • (1983) Ann. Probab. , vol.11 , pp. 457-490
    • Kaimanovich, V.A.1    Vershik, A.M.2
  • 41
    • 85008070306 scopus 로고
    • Classification of paragroup actions on subfactors
    • 41. Y. Kawahigashi, Classification of paragroup actions on subfactors, Publ. Res. Inst. Math. Sci. 31 (1995), 481-517.
    • (1995) Publ. Res. Inst. Math. Sci. , vol.31 , pp. 481-517
    • Kawahigashi, Y.1
  • 42
    • 0010049716 scopus 로고
    • Reduction theory on the relative entropy
    • 42. S. Kawakami and H. Yoshida, Reduction theory on the relative entropy, Math. Japon. 33 (1988), 975-990.
    • (1988) Math. Japon. , vol.33 , pp. 975-990
    • Kawakami, S.1    Yoshida, H.2
  • 43
    • 0001642071 scopus 로고    scopus 로고
    • Sector theory and automorphisms for factor-subfactor pairs
    • 43. H. Kosaki, Sector theory and automorphisms for factor-subfactor pairs, J. Math. Soc. Japan, 48 (1996), 427-454.
    • (1996) J. Math. Soc. Japan , vol.48 , pp. 427-454
    • Kosaki, H.1
  • 44
    • 0001510118 scopus 로고
    • A remark on the minimal index of subfactors
    • 44. H. Kosaki and R. Longo, A remark on the minimal index of subfactors, J. Funct. Anal. 107 (1992), 458-470.
    • (1992) J. Funct. Anal. , vol.107 , pp. 458-470
    • Kosaki, H.1    Longo, R.2
  • 46
    • 0030295440 scopus 로고    scopus 로고
    • On automorphisms of subfactors
    • 46. P. H. Loi, On automorphisms of subfactors, J. Funct. Anal. 141 (1996), 275-293.
    • (1996) J. Funct. Anal. , vol.141 , pp. 275-293
    • Loi, P.H.1
  • 47
    • 0000704523 scopus 로고
    • λ factors of index 4
    • λ factors of index 4, Pacific J. Math. 165 (1994), 321-345.
    • (1994) Pacific J. Math. , vol.165 , pp. 321-345
    • Loi, P.H.1
  • 48
    • 51249174399 scopus 로고
    • Index of subfactors and statistics of quantum fields. II
    • 48. R. Longo, Index of subfactors and statistics of quantum fields. II, Commun. Math. Phys. 130 (1990), 285-309.
    • (1990) Commun. Math. Phys. , vol.130 , pp. 285-309
    • Longo, R.1
  • 49
    • 0002257234 scopus 로고
    • Minimal index and braided subfactors
    • 49. R. Longo, Minimal index and braided subfactors, J. Funct. Anal. 109 (1992), 98-112.
    • (1992) J. Funct. Anal. , vol.109 , pp. 98-112
    • Longo, R.1
  • 50
    • 0000840618 scopus 로고
    • Quantized groups, string algebras and Galois theory for algebras
    • D. E. Evans and M. Takesaki, London Math. Soc. Lect. Note Ser. 136
    • 50. A. Ocneanu, Quantized groups, string algebras and Galois theory for algebras, in Operator Algebras and Applications Vol. 2, eds. D. E. Evans and M. Takesaki, London Math. Soc. Lect. Note Ser. 136, 1988, pp. 119-172.
    • (1988) Operator Algebras and Applications , vol.2 , pp. 119-172
    • Ocneanu, A.1
  • 55
    • 0000549795 scopus 로고
    • Sousfacteurs, actions des groupes et cohomologie
    • 55. S. Popa, Sousfacteurs, actions des groupes et cohomologie, C. R. Acad. Sci. Paris Sér. I 309 (1989), 771-776.
    • (1989) C. R. Acad. Sci. Paris Sér. I , vol.309 , pp. 771-776
    • Popa, S.1
  • 56
    • 0000307054 scopus 로고
    • Markov traces on universal Jones algebras and subfactors of finite index
    • 56. S. Popa, Markov traces on universal Jones algebras and subfactors of finite index, Invent. Math. 111 (1993), 375-405.
    • (1993) Invent. Math. , vol.111 , pp. 375-405
    • Popa, S.1
  • 57
    • 0000934215 scopus 로고
    • Classification of amenable subfactors of type II
    • 57. S. Popa, Classification of amenable subfactors of type II, Acta Math. 172 (1994), 163-255.
    • (1994) Acta Math. , vol.172 , pp. 163-255
    • Popa, S.1
  • 58
    • 0001110696 scopus 로고
    • Symmetric enveloping algebras, amenability and AFD properties for subfactors
    • 58. S. Popa, Symmetric enveloping algebras, amenability and AFD properties for subfactors, Math. Res. Lett. 1 (1994), 409-425.
    • (1994) Math. Res. Lett. , vol.1 , pp. 409-425
    • Popa, S.1
  • 59
    • 0001817855 scopus 로고
    • Approximate innerness and central freeness for subfactors: A classification result
    • H. Araki et al., World Scientific, Singapore
    • 59. S. Popa, Approximate innerness and central freeness for subfactors: a classification result, in Subfactors, eds. H. Araki et al., World Scientific, Singapore, 1994, pp. 274-293.
    • (1994) Subfactors , pp. 274-293
    • Popa, S.1
  • 60
    • 0000715340 scopus 로고
    • An axiomatization of the lattice of higher relative commutants of a subfactor
    • 60. S. Popa, An axiomatization of the lattice of higher relative commutants of a subfactor, Invent. Math. 120 (1995), 427-445.
    • (1995) Invent. Math. , vol.120 , pp. 427-445
    • Popa, S.1
  • 63
    • 0000408094 scopus 로고
    • Actions of compact Lie groups on von Neumann algebras
    • 63. S. Popa and A. Wassermann, Actions of compact Lie groups on von Neumann algebras, C. R. Acad. Sci. Paris Sér.I 315 (1992), 421-426.
    • (1992) C. R. Acad. Sci. Paris Sér.I , vol.315 , pp. 421-426
    • Popa, S.1    Wassermann, A.2
  • 64
    • 0030211228 scopus 로고    scopus 로고
    • Amenability of Hopf von Neumann algebras and Kac algebras
    • 64. Z. J. Ruan, Amenability of Hopf von Neumann algebras and Kac algebras, J. Funct. Anal. 139 (1996), 466-499.
    • (1996) J. Funct. Anal. , vol.139 , pp. 466-499
    • Ruan, Z.J.1
  • 65
    • 0001338026 scopus 로고    scopus 로고
    • Commuting co-commuting squares and finite dimensional Kac algebras
    • 65. T. Sano, Commuting co-commuting squares and finite dimensional Kac algebras, Pacific J. Math. 172 (1996), 243-253.
    • (1996) Pacific J. Math. , vol.172 , pp. 243-253
    • Sano, T.1
  • 66
    • 0000952157 scopus 로고
    • Angles between two subfactors
    • 66. T. Sano and Y. Watatani, Angles between two subfactors, J. Operator Theory 32 (1994), 209-241.
    • (1994) J. Operator Theory , vol.32 , pp. 209-241
    • Sano, T.1    Watatani, Y.2
  • 68
    • 84972487716 scopus 로고
    • Conditional expectation in an operator algebra, II
    • 68. H. Umegaki, Conditional expectation in an operator algebra, II, Tôhoku Math. J. 8 (1956), 86-100.
    • (1956) Tôhoku Math. J. , vol.8 , pp. 86-100
    • Umegaki, H.1
  • 69
    • 0001371204 scopus 로고
    • Long range estimates for Markov chains
    • 69. N. Th. Varopoulos, Long range estimates for Markov chains, Bull. Sci. Math. 109 (2) (1985), 225-252.
    • (1985) Bull. Sci. Math. , vol.109 , Issue.2 , pp. 225-252
    • Varopoulos, N.Th.1
  • 71
    • 0000488814 scopus 로고
    • Coactions and Yang-Baxter equations for ergodic actions and subfactors
    • D. E. Evans and M. Takesaki, London Math. Soc. Lect. Note Ser. 136
    • 71. A. Wassermann, Coactions and Yang-Baxter equations for ergodic actions and subfactors, in Operator Algebras and Applications Vol. 2, eds. D. E. Evans and M. Takesaki, London Math. Soc. Lect. Note Ser. 136, 1988, pp. 203-236.
    • (1988) Operator Algebras and Applications , vol.2 , pp. 203-236
    • Wassermann, A.1
  • 72
    • 0009979542 scopus 로고
    • An estimate of the depth from an intermediate subfactor
    • 72. J. Wierzbicki, An estimate of the depth from an intermediate subfactor, Publ. Res. Inst. Math. Sci. 30 (1994), 1139-1144.
    • (1994) Publ. Res. Inst. Math. Sci. , vol.30 , pp. 1139-1144
    • Wierzbicki, J.1
  • 73
    • 0010017262 scopus 로고
    • 1-subfactors by strongly outer actions
    • 1-subfactors by strongly outer actions, Trans. Amer. Math. Soc. 347 (1995), 985-991.
    • (1995) Trans. Amer. Math. Soc. , vol.347 , pp. 985-991
    • Winsløw, C.1
  • 74
    • 0002768694 scopus 로고
    • Random walks on infinite graphs and groups - A survey on selected topics
    • 74. W. Woess, Random walks on infinite graphs and groups - a survey on selected topics, Bull. London Math. Soc. 26 (1994), 1-60.
    • (1994) Bull. London Math. Soc. , vol.26 , pp. 1-60
    • Woess, W.1
  • 75
    • 1542483491 scopus 로고
    • Compact matrix pseudogroups
    • 75. S. L. Woronowicz, Compact matrix pseudogroups, Commun. Math. Phys. 111 (1987), 613-665.
    • (1987) Commun. Math. Phys. , vol.111 , pp. 613-665
    • Woronowicz, S.L.1
  • 76
    • 0001671457 scopus 로고
    • A note on Ocneanu's approach to Jones' index theory
    • 76. S. Yamagami, A note on Ocneanu's approach to Jones' index theory, Int. J. Math. 4 (1993), 859-871.
    • (1993) Int. J. Math. , vol.4 , pp. 859-871
    • Yamagami, S.1
  • 77
    • 0000970131 scopus 로고
    • Entropy of certain noncommutative shifts
    • 77. H. S. Yin, Entropy of certain noncommutative shifts, Rockey Mountain J. Math. 20 (1990), 651-656.
    • (1990) Rockey Mountain J. Math. , vol.20 , pp. 651-656
    • Yin, H.S.1


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