Locally compact quantum groups

 Access to full text

 Full (PDF)

1. [1] ABE E., Hopf Algebras, Cambridge Tracts in Mathematics, Vol. 74, Cambridge University Press, Cambridge, 1980. Zbl0476.16008MR83a:16010
2. [2] BAAJ S., Représentation régulière du groupe quantique des déplacements de Woronowicz, Astérisque 232 (1995) 11-48. Zbl0840.46036MR97a:46107
3. [3] BAAJ S., Représentation régulière du groupe quantique Eµ(2), C. R. Acad. Sci. Paris, Série I 314 (1992) 1021-1026. Zbl0771.17011MR93f:46106
4. [4] BAAJ S., Multiplicateurs non bornés, Thèse 3ème cycle, Université Paris-6, 1980. 
5. [5] BAAJ S., Prolongement d'un poids, C. R. Acad. Sci., Paris, Série A 288 (1979) 1013-1015. Zbl0414.46046MR80d:46108
6. [6] BAAJ S., SKANDALIS G., Unitaires multiplicatifs et dualité pour les produits croisés de C*-algèbres, Ann. Scient. Éc. Norm. Sup., 4e série 26 (1993) 425-488. Zbl0804.46078MR94e:46127
7. [7] BANICA T., Le groupe quantique compact libre U(n), Commun. Math. Phys. 190 (1997) 143-172. Zbl0906.17009MR99k:46095
8. [8] BUSBY R.C., Double centralizers and extensions of C*-algebras, Trans. Amer. Math. Soc. 132 (1968) 79-99. Zbl0165.15501MR37 #770
9. [9] CIORĂNESCU I., ZSIDÓ L., Analytic generators for one-parameter groups, Tôhoku Math. J. 28 (1976) 327-362. Zbl0361.47014MR55 #3872
10. [10] COMBES F., Poids associé à une algèbre hilbertienne à gauche, Compos. Math. 23 (1971) 49-77. Zbl0208.38201MR44 #5786
11. [11] COMBES F., Poids sur une C*-algèbre, J. Math. Pures et Appl. 47 (1968) 57-100. Zbl0165.15401MR38 #5016
12. [12] D'ANTONI C., ZSIDÓ L., Groups of linear isometries on multiplier C*-algebras, Pac. J. Math. 193 (2) (2000) 279-306. Zbl1088.46512MR2001g:46122
13. [13] DRINFEL'D V.G., Quantum groups, Proceedings ICM Berkeley (1986) 798-820. Zbl0667.16003MR89f:17017
14. [14] EFFROS E., RUAN Z.-J., Discrete quantum groups I : The Haar measure, Int. J. Math. 5 (5) (1994) 681-723. Zbl0824.17020MR95j:46089
15. [15] ENOCK M., SCHWARTZ J.-M., Kac Algebras and Duality of Locally Compact Groups, Springer-Verlag, Berlin, 1992. Zbl0805.22003MR94e:46001
16. [16] ENOCK M., VALLIN J.-M., C*-algèbres de Kac et algèbres de Kac, Proc. London Math. Soc. 66 (3) (1993) 619-650. Zbl0792.46040MR94e:46101
17. [17] HAAGERUP U., Operator-valued weights in von Neumann algebras, I, J. Funct. Anal. 32 (1979) 175-206. Zbl0426.46046MR81e:46049a
18. [18] HAAGERUP U., Normal weights on W*-algebras, J. Funct. Anal. 19 (1975) 302-317. Zbl0304.46043MR52 #1338
19. [19] KIRCHBERG E., Lecture on the conference 'Invariants in operator algebras', Copenhagen, August 1992. 
20. [20] KOELINK H.T., Addition formula for a 2-parameter family of Askey-Wilson polynomials, Preprint, KU Leuven, 1994. Zbl0844.33011
21. [21] KOELINK H.T., On quantum groups and q-special functions, PhD-thesis, Rijksuniversiteit Leiden, 1991. Zbl0721.17014
22. [22] KOELINK H.T., VERDING J., Spectral analysis and the Haar functional on the quantum SU(2) group, Commun. Math. Phys. 177 (1996) 399-415. Zbl0848.22029MR97a:33048
23. [23] KUSTERMANS J., Locally compact quantum groups in the universal setting, Int. J. Math., to appear. #math/9902015. Zbl1111.46311
24. [24] KUSTERMANS J., KMS-weights on C*-algebras, Preprint, Odense Universitet, 1997. #funct-an/9704008. 
25. [25] KUSTERMANS J., One-parameter representations on C*-algebras, Preprint, Odense Universitet, 1997. #funct-an/9707010. 
26. [26] KUSTERMANS J., The functional calculus of regular operators on Hilbert C*-modules revisited, Preprint, Odense Universitet, 1997. #funct-an/9706007. 
27. [27] KUSTERMANS J., VAES S., A simple definition for locally compact quantum groups, C. R. Acad. Sci. Paris, Série I 328 (10) (1999) 871-876. Zbl0957.46037MR2000i:46051
28. [28] KUSTERMANS J., VAES S., The operator algebra approach to quantum groups, Proc. Natl. Acad. Sc. 97 (2) (2000) 547-552. Zbl0978.46044MR2001m:46118
29. [29] KUSTERMANS J., VAES S., Locally compact quantum groups in the von Neumann algebraic setting, Preprint, KU, Leuven, 2000. #math.OA/0005219. Zbl1034.46067
30. [30] KUSTERMANS J., VAES S., Weight theory for C*-algebraic quantum groups, Preprint, KU Leuven & University College Cork, 1999. #math/9901063. Zbl0957.46037
31. [31] KUSTERMANS J., VAN DAELE A., C*-algebraic quantum groups arising from algebraic quantum groups, Int. J. Math. 8 (8) (1997) 1067-1139. #q-alg/9611023. Zbl1009.46038MR99a:46130
32. [32] LANCE C., Hilbert C*-Modules. A Toolkit for Operator Algebraists, London Math. Soc. Lect. Note Series, Vol. 210, Cambridge University Press, Cambridge, 1995. Zbl0822.46080
33. [33] MASUDA T., NAKAGAMI Y., A von Neumann algebra framework for the duality of the quantum groups, Publ. RIMS, Kyoto University 30 (1994) 799-850. Zbl0839.46055MR96b:46103
34. [34] MASUDA T., NAKAGAMI Y., WORONOWICZ S.L., Lectures at the Fields Institute and at the University of Warsaw, 1995. 
35. [35] PEDERSEN G.K., C*-Algebras and their Automorphism Groups, Academic Press, London, 1979. Zbl0416.46043MR81e:46037
36. [36] PEDERSEN G.K., TAKESAKI M., The Radon-Nikodym theorem for von Neumann algebras, Acta Math. 130 (1973) 53-87. Zbl0262.46063MR54 #948
37. [37] PODLEŚ P., Quantum spheres, Lett. Math. Phys. 14 (1987) 193-202. Zbl0634.46054MR89b:46081
38. [38] PODLEŚ P., WORONOWICZ S.L., Quantum deformation of Lorentz group, Commun. Math. Phys. 130 (1990) 381-431. Zbl0703.22018MR91f:46100
39. [39] QUAEGEBEUR J., VERDING J., A construction for weights on C*-algebras. Dual weights for C*-crossed products, Int. J. Math. 10 (1) (1999) 129-157. Zbl0956.46046MR2001d:46099
40. [40] QUAEGEBEUR J., VERDING J., Left invariant weights and the left regular corepresentation for locally compact quantum semi-groups, Preprint, KU Leuven, 1994. 
41. [41] RIEFFEL M.A., Compact quantum groups associated with toral subgroups, Contemp. Math. 145 (1993) 465-491. Zbl0795.17017MR94i:22022
42. [42] RIEFFEL M.A., Deformation quantization of Heisenberg manifolds, Commun. Math. Phys. 122 (1989) 531-562. Zbl0679.46055MR90e:46060
43. [43] RIEFFEL M.A., Integrable and proper actions on C*-algebras, and square-integrable representations of groups, 1998. #math/9809098. Zbl1047.22004
44. [44] RIEFFEL M.A., Some solvable quantum groups. Operator algebras and topology, in : Arveson W.B. et al. (Eds.), Proceedings of the OATE 2 Conference Bucharest, Romania, 1989, Pitman Research Notes in Mathematics, Vol. 270, 1992, pp. 146-159. Zbl0804.17010
45. [45] SAKAI S., C*-Algebras and W*-Algebras, Springer-Verlag, Berlin, 1971. Zbl0219.46042MR56 #1082
46. [46] STRATILA S., Modular Theory in Operator Algebras, Abacus Press, Tunbridge Wells, England, 1981. Zbl0504.46043MR85g:46072
47. [47] STRATILA S., ZSIDÓ L., Lectures on von Neumann Algebras, Abacus Press, Tunbridge Wells, England, 1979. Zbl0391.46048MR81j:46089
48. [48] TAKESAKI M., Theory of Operator Algebras I, Springer-Verlag, New York, 1979. Zbl0436.46043MR81e:46038
49. [49] TAYLOR D.C., The strict topology for double centralizer algebras, Trans. Amer. Math. Soc. 150 (1970) 633-643. Zbl0204.14701MR44 #7302
50. [50] VAES S., The unitary implementation of a locally compact quantum group action, J. Funct. Anal., to appear. #math.OA/0005262. Zbl1011.46058
51. [51] VAES S., Examples of locally compact quantum groups through the bicrossed product construction, in : Proceedings of the XIIIth International Conference on Mathematical Physics, London, 2000, to appear. Zbl1045.46042
52. [52] VAES S., A Radon-Nikodym theorem for von Neumann algebras, J. Oper. Th., to appear. #math.OA/9811122. Zbl0995.46042
53. [53] VAES S., Hopf C*-algebras, Masters Thesis, KU Leuven, 1998. 
54. [54] VAES S., VAN DAELE A., Hopf C*-algebras, Proc. London Math. Soc., to appear. #math.OA/9907030. Zbl1028.46100
55. [55] VAINERMAN L.I., KAC G.I., Nonunimodular ring-groups and Hopf-von Neumann algebras, Math. USSR, Sbornik 23 (1974) 185-214. Zbl0309.46052MR50 #536
56. [56] VAINERMAN G.I., KAC G.I., Nonunimodular ring-groups and Hopf-von Neumann algebras, Soviet Math. Dokl. 14 (1973) 1144-1148. Zbl0296.46072
57. [57] VAKSMAN L.L., SOIBEL'MAN Y.S., Algebra of functions on the quantum group SU(2), Funct. Anal. Appl. 22 (1988) 170-181. Zbl0679.43006MR90f:17019
58. [58] VALLIN J.-M., C*-algèbres de Hopf et C*-algèbres de Kac, Proc. London Math. Soc. 50 (3) (1985) 131-174. Zbl0577.46063MR86f:46072
59. [59] VAN DAELE A., An algebraic framework for group duality, Adv. in Math. 140 (1998) 323-366. Zbl0933.16043MR2000g:16045
60. [60] VAN DAELE A., Discrete quantum groups, J. Algebra 180 (1996) 431-444. Zbl0864.17012MR97a:16076
61. [61] VAN DAELE A., The Haar measure on a compact quantum group, Proc. Amer. Math. Soc. 123 (1995) 3125-3128. Zbl0844.46032MR95m:46097
62. [62] VAN DAELE A., Multiplier Hopf Algebras, Trans. Amer. Math. Soc. 342 (1994) 917-932. Zbl0809.16047MR94h:16075
63. [63] VAN DAELE A., WANG S.Z., Universal quantum groups, Int. J. Math. 7 (2) (1996) 255-263. Zbl0870.17011MR97d:46090
64. [64] VAN DAELE A., WORONOWICZ S.L., Duality for the quantum E(2) group, Pacific J. Math. 173 (2) (1996) 375-385. Zbl0868.17013MR97d:46091
65. [65] VERDING J., Weights on C*-algebras, PhD Thesis, KU Leuven, 1995. Zbl0956.46046
66. [66] WANG S.Z., Free Products of compact quantum groups, Commun. Math. Phys. 167 (1995) 671-692. Zbl0838.46057MR95k:46104
67. [67] WORONOWICZ S.L., Compact quantum groups, in : Symétries Quantiques (Les Houches, 1995), North-Holland, Amsterdam, 1998, pp. 845-884. Zbl0997.46045MR99m:46164
68. [68] WORONOWICZ S.L., From multiplicative unitaries to quantum groups, Int. J. Math. 7 (1) (1996) 127-149. Zbl0876.46044MR96k:46136
69. [69] WORONOWICZ S.L., Quantum E(2) group and its Pontryagin dual, Lett. Math. Phys. 23 (1991) 251-263. Zbl0752.17017MR93b:17058
70. [70] WORONOWICZ S.L., Unbounded elements affiliated with C*-algebras and non-compact quantum groups, Commun. Math. Phys. 136 (1991) 399-432. Zbl0743.46080MR92b:46117
71. [71] WORONOWICZ S.L., Tannaka-Krein duality for compact matrix pseudogroups. Twisted SU(N) groups, Invent. Math. 93 (1988) 35-76. Zbl0664.58044MR90e:22033
72. [72] WORONOWICZ S.L., Compact matrix pseudogroups, Commun. Math. Phys. 111 (1987) 613-665. Zbl0627.58034MR88m:46079
73. [73] WORONOWICZ S.L., Twisted SU(2) group. An example of a non-commutative differential calculus, Publ. RIMS, Kyoto University 23 (1987) 117-181. Zbl0676.46050MR88h:46130
74. [74] WORONOWICZ S.L., Pseudospaces, pseudogroups and Pontrjagin duality, in : Proceedings of the International Conference on Mathematical Physics (Lausanne, 1979), Lecture Notes in Physics, Vol. 116, 1980, pp. 407-412. Zbl0513.46046

1. J. Martin Lindsay, Adam G. Skalski, Quantum stochastic convolution cocycles I
2. Jean-Michel Vallin, Measured quantum groupoids associated with matched pairs of locally compact groupoids
3. Michel Enock, The unitary implementation of a measured quantum groupoid action
4. Georges Skandalis, Géométrie non commutative, opérateur de signature transverse et algèbres de Hopf