Publications of the Research Institute for Mathematical Sciences

Classification of paragroup actions in subfactors

Yasuyuki Kawahigashi

Source: Publ. Res. Inst. Math. Sci. Volume 31, Number 3 (1995), 481-517.

Primary Subjects: 46L37

Full-text: Open access

Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.prims/1195164051
Mathematical Reviews number (MathSciNet): MR1355948
Zentralblatt MATH identifier: 0837.46046
Digital Object Identifier: doi:10.2977/prims/1195164051

References

[1] Alexander, J. W., The combinatorial theory of complexes, Ann, Math., (2) 31 (1930), 294-322.
Mathematical Reviews (MathSciNet): MR1502943
Jahrbuch database (Zbl): 56.0497.02
[2] Andrews, G. E., Baxter, R. J. and Forrester, P. J., Eight vertex SOS model and generalized Rogers-Ramanujan type identities, J. Stat. Phys., 35 (1984), 193-266.
Mathematical Reviews (MathSciNet): MR748075
Zentralblatt MATH: 0589.60093
[3] Bisch, D., On the existence of central sequences in subfactors, Trans. Amer. Math. Soc., 321 (1990), 117-128.
Mathematical Reviews (MathSciNet): MR1005075
Zentralblatt MATH: 0711.46048
[4] Bisch, D., On the structure of finite depth subfactors, "Algebraic methods in operator theory", Birkhauser (1994), 175-194.
Mathematical Reviews (MathSciNet): MR1284945
Zentralblatt MATH: 0809.46069
[5] Bisch, D., A note on intermediate subfactors, Pac. J. Math., 163 (1994), 201-216.
Mathematical Reviews (MathSciNet): MR1262294
Zentralblatt MATH: 0814.46053
[6] de Boer, J. and Goeree,J., Markov traces and II1 factors in conformal field theory, Comm. Math. Phys., 139 (1991), 267-304.
Mathematical Reviews (MathSciNet): MR1120140
Zentralblatt MATH: 0760.57002
[7] Choda, M. and Kosaki, H., Strongly outer actions for inclusion of factors, J. Funct. Anal., 122 (1994), 315-332.
Mathematical Reviews (MathSciNet): MR1276161
Zentralblatt MATH: 0802.46072
[8] Connes, A., Outer conjugacy classes of automorphisms of factors, Ann. Sci. Ecole Norm. Sup., 8 (1975), 383-419.
Mathematical Reviews (MathSciNet): MR394228
Zentralblatt MATH: 0342.46052
[9] Di Francesco, P. and Zuber, J.-B., SU(N) lattice integrable models associated with graphs, Nucl. Phys., B338 (1990), 602-646.
Mathematical Reviews (MathSciNet): MR1063590
[10] Evans, D. E. and Kawahigashi, Y., Orbifold subfactors from Hecke algebras, Comm. Math. Phys., 165 (1994), 445-484.
Mathematical Reviews (MathSciNet): MR1301620
Zentralblatt MATH: 0805.46077
[11] Evans, D. E. and Kawahigashi, From subfactors to 3-dimensional topological quantum field theories and back, to appear in Internal. J. Math.
Zentralblatt MATH: 0844.57014
[12] Evans, D. E. and Kawahigashi, The E7 commuting squares produce D10 as principal graph, Publ. RIMS, Kyoto Univ., 30 (1994), 151-166.
Mathematical Reviews (MathSciNet): MR1266388
Zentralblatt MATH: 0814.46054
[13] Evans, D. E. and Kawahigashi, Subfactors and conformal field theory, in Quantum and non-commutative analysis, Kluwer Academic (1993), 341-369.
Mathematical Reviews (MathSciNet): MR1276304
Zentralblatt MATH: 0848.46039
[14] Fendley, P., New exactly solvable orbifold models, J. Phys., A22 (1989), 4633-4642.
Mathematical Reviews (MathSciNet): MR1022137
Zentralblatt MATH: 0732.22018
[15] Fendley, P. and Ginsparg, P., Non-critical orbifolds, Nucl. Phys., B324 (1989), 549-580.
[16] Goodman, F., de la Harpe, P. and Jones, V. F. R., Coxeter graphs and towers of algebras, MSRI Publications 14, Springer, 1989.
Mathematical Reviews (MathSciNet): MR999799
Zentralblatt MATH: 0698.46050
[17] Haagerup, U., Principal graphs of subfactors in the index range 4 < [M: N] < 3 + V2, Subfactors, World Scientific, (1994) 1-38.
Mathematical Reviews (MathSciNet): MR1317352
Zentralblatt MATH: 0933.46058
[18] Izumi, M., Application of fusion rules to classification of subfactors, Publ. RIMS, Kyoto Unvi., 27 (1991), 953-994.
Mathematical Reviews (MathSciNet): MR1145672
Zentralblatt MATH: 0765.46048
[19] Izumi, M., On flatness of the Coxeter graph E8, Pac. J. Math., 166 (1994), 305-327.
Mathematical Reviews (MathSciNet): MR1313457
Zentralblatt MATH: 0822.46073
[20] Jones, V. F. R., Actions of finite groups on the hyperfinite type II, factor, Mem. Amer. Math. Soc., 28 No. 237 (1980), 1-70.
Mathematical Reviews (MathSciNet): MR587749
Zentralblatt MATH: 0454.46045
[21] Jones, V. F. R., Index for subfactors, Invent. Math., 72 (1983), 1-15.
Mathematical Reviews (MathSciNet): MR696688
Zentralblatt MATH: 0508.46040
[22] Jones, V. F. R., A polynomial invariant for knots via von Neumann algebras, Bull. Amer. Math. Soc., 12 (1985), 103-112.
Mathematical Reviews (MathSciNet): MR766964
Zentralblatt MATH: 0564.57006
[23] Kawahigashi, Y., Automorphisms commuting with a conditional expectation onto a subfactor with finiteindex, J. Operator Theory, 28 (1992), 127-145.
Mathematical Reviews (MathSciNet): MR1259921
Zentralblatt MATH: 0845.46032
[24] Kawahigashi, Y., On flatness of Ocneanu's connections on the Dynkin diagrams and classification of subfactors, J. Funct. Anal., 127 (1995), 63-107.
Mathematical Reviews (MathSciNet): MR1308617
Zentralblatt MATH: 0829.46048
[25] Kawahigashi, Y., Exactly solvable orbifold models and subfactors, in Functional Analysis and Related Topics, Lect. Notes, in Math., Springer Verlag, 1540, (1992), 127-147.
Mathematical Reviews (MathSciNet): MR1225815
Zentralblatt MATH: 0802.46074
[26] Kawahigashi, Y., Centrally trivial automorphisms and an analogue of Connes' X(M) for subfactors, Duke Math. J., 71 (1993), 93-118.
Mathematical Reviews (MathSciNet): MR1230287
Zentralblatt MATH: 0830.46051
[27] Kawahigashi, Y., Paragroups as quantized Galois groups of subfactors, to appear in Sugaku Exp.
Mathematical Reviews (MathSciNet): MR1256473
[28] Kirillov A. N. and Reshetikhin, N. Yu., Representations of the algebra U ( ( s l 2 ), q-orthogonal polynomials and invariants for links, in Infinite dimensional Lie algebras and groups (V. G. Kac, ed.), Adv. Ser. Math. Phys., 7 (1988), 285-339.
Zentralblatt MATH: 0742.17018
[29] Kosaki, H., Automorphisms in irreducible decompositions of sectors, in Quantum and non-commutative analysis, Kluwer Academic (1993), 305-316.
Mathematical Reviews (MathSciNet): MR1276299
Zentralblatt MATH: 0846.46042
[30] Rostov, I., Free field presentation of the An coset models on the torus, Nucl. Phys., B300 (1988), 559-587.
Mathematical Reviews (MathSciNet): MR965912
[31] Loi, P. H., On automorphisms of subfactors,preprint 1990.
Mathematical Reviews (MathSciNet): MR1418506
Zentralblatt MATH: 0923.46063
[32] Moore G., and Seiberg, N., Classical and quantum conformal field theory, Comm. Math. Phys., 123 (1989), 177-254.
Mathematical Reviews (MathSciNet): MR1002038
Zentralblatt MATH: 0694.53074
[33] Nitica, V. and Torok, A., in preparation.
[34] Ocneanu, A., Actions of discrete amenable groups on factors, Lect. Notes in Math., Springer, Berlin, 1138, (1985).
Mathematical Reviews (MathSciNet): MR807949
Zentralblatt MATH: 0608.46035
[35] Ocneanu, A., Quantized group, string algebras and Galois theory for algebras, in Operator algebras and applications, 2 (Warwick, 1987), London Math. Soc. Lect. Note Series, Cambridge University Press, 136 (1988), 119-172.
Mathematical Reviews (MathSciNet): MR996454
Zentralblatt MATH: 0696.46048
[36] Ocneanu, A., Graph geometry, quantized groups and nonamenable subfactors, Lake Tahoe Lectures, June-July, 1989.
[37] Ocneanu, A., Quantum symmetry, differential geometry of finite graphs and classification of subfactors, University of Tokyo Seminary Notes 45, (Notes recorded by Y. Kawahigashi), 1991.
[38] Ocneanu, A., An invariant coupling between 3-manifolds and subfactors, with connections to topological and conformal quantum field theory, preprint 1991.
[39] Okamoto, S., Invariants for subfactors arising from Coxeter graphs, in Current Topics in Operator Algebras, World Scientific Publishing, (1991), 84-103.
Mathematical Reviews (MathSciNet): MR1193932
Zentralblatt MATH: 0809.46072
[40] Pimsner, M. and Popa, S., Entropy and index for subfactors, Ann. Scient. Ec. Norm. Sup., 19 (1986), 57-106.
Mathematical Reviews (MathSciNet): MR860811
Zentralblatt MATH: 0646.46057
[41] Pimsner, M. and Popa, Iterating the basic constructions, Trans. Amer. Math. Soc., 310 (1988), 127-134.
Mathematical Reviews (MathSciNet): MR965748
Zentralblatt MATH: 0706.46047
[42] Popa, S., Correspondences,preprint 1986.
[43] Popa, S., Classification of subfactors: reduction to commuting squares, Invent. Math., 101 (1990), 19-43.
Mathematical Reviews (MathSciNet): MR1055708
Zentralblatt MATH: 0757.46054
[44] Popa, S., Classification of amenable subfactors of type II, Acta Math., 172 (1994), 352-445.
Mathematical Reviews (MathSciNet): MR1278111
Zentralblatt MATH: 0853.46059
[45] Popa, S., On the classification of actions of amenable groups on subfactors, C. R. Acad. Sc. Paris., 315 (1992), 295-299.
Mathematical Reviews (MathSciNet): MR1179723
Zentralblatt MATH: 0766.43002
[46] Popa, S., Classification of actions of discrete amenable groups on amenable subfactors of type II, preprint 1992.
Mathematical Reviews (MathSciNet): MR1179723
Zentralblatt MATH: 0922.46056
[47] Popa, S., Approximate innerness and central freeness for subfactors: A classification result, Subfactors, World Scientific (1994), 274-293.
Mathematical Reviews (MathSciNet): MR1317367
Zentralblatt MATH: 0928.46039
[48] Popa, S., Classification of subfactors of finite depth of the hyperfinite type III1 factor, to appear in C. R. Acad. Sc. Paris.
Zentralblatt MATH: 0757.46054
[49] Reshetikhin, N. Yu. and Turaev, V. G., Invariants of 3-manifolds via link polynomials and quantum groups, Invent. Math., 103 (1991), 547-597.
Mathematical Reviews (MathSciNet): MR1091619
Zentralblatt MATH: 0725.57007
[50] Roche, Ph., Ocneanu cell calculus and integrable lattice models, Comm. Math, Phys., 127 (1990), 395^24.
Mathematical Reviews (MathSciNet): MR1037111
Zentralblatt MATH: 0709.60536
[51] Sano, T., Commuting co-commuting squares and finite dimensional Kac algebras, preprint 1993.
Mathematical Reviews (MathSciNet): MR1379296
Zentralblatt MATH: 0851.46046
[52] Sano, T. and Watatani, Y., Angles between two subfactors, J. Operator Theory, 32 (1994), 209-241.
Mathematical Reviews (MathSciNet): MR1338739
Zentralblatt MATH: 0838.46052
[53] Schou, J., Commuting squares and index for subfactors, Ph. D. Thesis, Odense University, 1990.
[54] Sunder, V. S. and Vijayarajan, A. K., On the non-occurrence of the Coxeter graphs /J,n+|, E7, D2n+l as principal graphs of an inclusion of II, factors, Pac. J. Math., 161 (1993), 185-200.
Mathematical Reviews (MathSciNet): MR1237144
Zentralblatt MATH: 0798.43005
[55] Turaev, V. G. and Viro, O. Y., State sum invariants of 3-manifolds and quantum 6j-symbols, Topology, 31 (1992), 865-902.
Mathematical Reviews (MathSciNet): MR1191386
Zentralblatt MATH: 0779.57009
[56] Wierzbicki, J., An estimate of the depth from an intermediate subfactor, preprint 1993.
Mathematical Reviews (MathSciNet): MR1322948
Zentralblatt MATH: 0831.46070
[57] Wierzbicki, J. and Watatani, Y., Commuting squares and relative entropy for two subfactors, preprint 1992.
Mathematical Reviews (MathSciNet): MR1354034
Zentralblatt MATH: 0899.46051
[58] Wenzl,H.,Hecke algebras of type An and subfactors, Invent. Math., 92 (1988), 345-383.
Mathematical Reviews (MathSciNet): MR936086
Zentralblatt MATH: 0663.46055
[59] Winslow, C., Approximately inner automorphisms on inclusions of type IIIy factors, Pac. J. Math., 166 (1994), 385-400.
Mathematical Reviews (MathSciNet): MR1313462
Zentralblatt MATH: 0822.46072
[60] Winslow, C., Strongly free actions on subfactors, Internat. J. Math., 4 (1993), 675-688.
Mathematical Reviews (MathSciNet): MR1232987
Zentralblatt MATH: 0802.46077
[61] Winslow, C., Crossed products of II1-subfactors by strongly outer actions, Proc. Amer. Math. Soc., 347 (1995), 985-991.
Mathematical Reviews (MathSciNet): MR1242110
Zentralblatt MATH: 0820.46061
[62] Witten, E., Quantum field theory and Jones polynomial, Comm. Math. Phys., 121 (1989), 351-399.
Mathematical Reviews (MathSciNet): MR990772
Zentralblatt MATH: 0667.57005
[63] Xu, F., Orbifold construction in subfactors, Comm. Math. Phys., 116 (1994), 237-254.
Mathematical Reviews (MathSciNet): MR1309549
Zentralblatt MATH: 0876.46039
[64] Xu, F., The flat parts of non-flat orbifolds, to appear in Pac. J. Math.
Mathematical Reviews (MathSciNet): MR1379298
Zentralblatt MATH: 0851.46044
[65] Yamagami, Y., A note on Ocneanu's approach to Jones' index theory, Internat. J. Math., 4 (1993), 859-871.
Mathematical Reviews (MathSciNet): MR1245354
Zentralblatt MATH: 0793.46040

2010 © Research Institute for Mathematical Sciences

Publications of the Research Institute for Mathematical Sciences

Publications of the Research Institute for Mathematical Sciences