Non-semi-regular quantum groups coming from number theory

Communications in Mathematical Physics

Volumn 235, Issue 1, 2003, Pages 139-167

  Baaj, Saad ^a   Skandalis, Georges ^b   Vaes, Stefaan ^b  

^a UNIVERSITÉ BLAISE PASCAL   (France)

^b INSTITUT DE MATHÉMATIQUES DE JUSSIEU   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038271922     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-002-0780-6     Document Type: Article

References (22)

1. Baaj, S.: Représentation régulière du groupe quantique des déplacements de Woronowicz. Astérisque 232, 11-48 (1995)
2. e série 26, 425-488 (1993)
3. Baaj, S., Skandalis, G.: Transformations pentagonales. C.R. Acad. Sci., Paris, Sér. I, 327, 623-628 (1998)
4. Baaj, S., Vaes, S.: Double crossed products of locally compact quantum groups. Preprint
5. Bost, J.-B., Connes, A.: Hecke algebras, type III factors and phase transitions with spontaneous symmetry breaking in number theory. Selecta Math. (N.S.) 1, 411-457 (1995)
6. Desmedt, P., Quaegebeur, J., Vaes, S.: Amenability and the bicrossed product construction. 111. J. Math., to appear
7. Enock, M., Schwartz, J.-M.: Kac Algebras and Duality of Locally Compact Groups. Berlin-Heidelberg-New York: Springer-Verlag, 1992
8. Pack, T.: Quelques remarques sur le spectre des C*-algèbres de feuilletages. Bull. Soc. Math. Belg. Sér. 836, 113-129 (1984)
9. Kac, G.I.: Ring groups and the principle of duality, I, II. Trans. Moscow Math. Soc., 291-339 (1963), 94-126 (1965)
10. Kac, G.I.: Extensions of groups to ring groups. Math. USSR Sbornik 5, 451-474 (1968)
11. Kac, G.I., Vainerman, L.I.: Nonunimodular ring groups and Hopf-von Neumann algebras. Math. USSR. Sbornik 23, 185-214 (1974)
12. Kashaev, R.M., Sergeev, S.M.: On pentagon, ten-term, and tetrahedron relations. Commun. Math. Phys. 195, 309-319 (1998)
13. Kustermans, J.: Locally compact quantum groups in the universal setting. Internat. J. Math. 12, 289-338 (2001)
14. e série 33, 837-934 (2000)
15. Kustermans, J., Vaes, S.: Locally compact quantum groups in the von Neumann algebraic setting. Math. Scand., to appear
16. Majid, S.: Hopf-von Neumann algebra bicrossproducts, Kac algebra bicrossproducts, and the classical Yang-Baxter equations. J. Fund. Anal. 95, 291-319 (1991)
17. Rieffel, M. A.: Strong Morita equivalence of certain transformation group C*-algebras. Math. Ann. 222, 71-97 (1976)
18. Takeuchi, M.: Matched pairs of groups and bismash products of Hopf algebras. Comm. Algebra 9, 841-882(1981)
19. Vaes, S., Vainerman, L.: Extensions of locally compact quantum groups and the bicrossed product construction. Adv. Math., to appear
20. Vaes, S., Vainerman, L.: On low-dimensional locally compact quantum groups. In: Locally Compact Quantum Groups and Groupoids, Proceedings of the Meeting of Theoretical Physicists and Mathematicians, Strasbourg, February 21-23, 2002., Ed. L. Vainerman, IRMA Lectures on Mathematics and Mathematical Physics. Berlin, New York: Walter de Gruyter, 2003. pp. 127-187
21. Woronowicz, S.L.: From multiplicative unitaries to quantum groups. Int. J. Math. 7(1), 127-149 (1996)
22. Woronowicz, S.L.: Twisted SU(2) group. An example of a non-commutative differential calculus. Publ. RIMS, Kyoto University 23, 117-181 (1987)