Locally compact quantum groups in the von Neumann algebraic setting

Mathematica Scandinavica

Volumn 92, Issue 1, 2003, Pages 68-92

  Kustermans, Johan ^a   Vaes, Stefaan ^b  

^a UNIVERSITY OF LEUVEN   (Belgium)

^b INSTITUT DE MATHÉMATIQUES DE JUSSIEU   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037278968     PISSN: 00255521     EISSN: None     Source Type: Journal    
DOI: 10.7146/math.scand.a-14394     Document Type: Article

References (19)

1. Baaj, S. and Skandalis, G., Unitaires multiplicatifs et dualité pour les produits croisés de C*-algèbres, Ann. Sci. École Norm. Sup. (4), 26 (1993), 425-488.
2. Enock, M. and Schwartz, J. -M., Produit croisé d'Une algèbre de von Neumann par une algèbre de Kac II, Publ. Res. Inst. Math. Sci. 16 (1980), 189-232.
3. Enock, M. and Schwartz, J. -M., Kac Algebras and Duality of Locally Compact Groups, Springer-Verlag, Berlin (1992).
4. Haagerup, U., Operator valued weights in von Neumann algebras I, J. Funct. Anal. 32 (1979), 175-206.
5. Kustermans, J., Induced corepresentations of locally compact quantum groups, J. Funct. Anal., to appear.
6. Kustermans, J., KMS-weights on C*-algebras, Preprint Odense Universitet (1997). #funct-an/9704008
7. Kustermans, J., One-parameter representations on C*-algebras, Preprint Odense Universitet (1997). #funct-an/9707010
8. Kustermans, J. and Vaes, S., Locally compact quantum groups, Ann. Sci. École Norm. Sup. (4) 33 (6) (2000), 837-934.
9. Kustermans, J. and Vaes, S., A simple definition for locally compact quantum groups, C. R. Acad. Sci., Paris Sér. I 328 (10) (1999), 871-876.
10. Kustermans, J. and Vaes, S., The operator algebra approach to quantum groups, Proc. Nat. Acad. Sci. USA 97 (2) (2000), 547-552.
11. Masuda, T. and Nakagami, Y., A von Neumann algebra framework for the duality of the quantum groups, Publ. Res. Inst. Math. Sci. 30 (1994), 799-850.
12. Stratila, S., Modular Theory in Operator Algebras, Abacus Press, Tunbridge Wells, England (1981).
13. Vaes, S., The unitary implementation of a locally compact quantum group action, J. Funct. Anal. 180 (2001), 426-480.
14. Vaes, S., A Radon-Nikodym theorem for von Neumann algebras, J. Operator Theory 46 (2001), 477-489.
15. Vainerman, L. I. and Kac, G. I., Nonunimodular ring-groups and Hopf-von Neumann algebras, Math. USSR-Sb. 23 (1974), 185-214.
16. Van Daele, A., An algebraic framework for group duality. Adv. Math. 140 (1998), 323-366.
17. Weil, A., L'Intégration dans les groupes topologiques et ses applications, Actualités. Sci. Indust. 1145, (1953).
18. Woronowicz, S. L., From multiplicative unitaries to quantum groups. Internat. J. Math. 7 (1996), 127-149.
19. Zsidó, L., On the equality of two weights, Rev. Roumaine Math. Pures Appl. 23 (1978), 631-646.