From double Lie groups to quantum groups

Fundamenta Mathematicae

Volumn 188, Issue , 2005, Pages 195-240

  Stachura, Piotr ^a,b,c  

^a George Washington University ^*

^b GEORGE WASHINGTON UNIVERSITY   (United States)

^c UNIVERSITY OF WARSAW   (Poland)

Author keywords

Double Lie group; Quantum group

Indexed keywords

EID: 33644510795     PISSN: 00162736     EISSN: None     Source Type: Journal    
DOI: 10.4064/fm188-0-10     Document Type: Article

References (19)

1. S. Baaj and G. Skandalis, Unitaires multiplicatifs et dualitŕ pour les produits croisés de C*-algèbres, Ann. Sci. École Norm. Sup. 26 (1993), 425-488.
2. A. Connes, Noncommutative Geometry, Academic Press, San Diego, 1994.
3. A. van Daele, Multiplier Hopf algebras, Trans. Amer. Math. Soc. 342 (1994), 917-932.
4. M. Enock and J.-M. Schwartz, Kac Algebras and Duality of Locally Compact Groups, Springer, 1992.
5. G. Kac, Extensions of groups to ring groups, Math. USSR-Sb. 5 (1968), 451-474.
6. J. H. Lu and A. Weinstein, Poisson Lie groups, dressing transformations and Bruhat decomposition, J. Differential Geom. 31 (1990), 501-526.
7. S. Majid, Physics for algebraists: Non-commutative and non-cocommutative Hopf algebras by a bicrossproduct construction, J. Algebra 130 (1990), 17-64.
8. _, Hopf-von Neumann algebra bicrossproducts, Kac algebra bicrossproducts and classical Yang-Baxter equations, J. Funct. Anal. 95 (1991), 291-319.
9. _, Foundations of Quantum Group Theory, Cambridge Univ. Press, 1995.
10. T. Masuda, Y. Nakagami and S. L. Woronowicz, C* -algebraic framework for the duality of quantum groups, Int. J. Math. 14 (2003), 903-1001.
11. J. Renault, Groupoid Approach to C*-Algebras, Lecture Notes in Math. 793, Springer, 1980.
12. P. Stachura, Manageability of multiplicative unitaries associated with double Lie groups, Lett. Math. Phys. 51 (2000), 135-143.
13. _, Differential groupoids and C* -algebras, math. QA/9905097;
14. for a short exposition see also: C*-algebra of a differential groupoid, Banach Center Publ. 51, Inst. Math., Polish Acad. Sci., 2000, 263-281.
15. S. Vaes and J. Kustermans, Locally compact quantum groups, Ann. Sci. École Norm. Sup. 33 (2000), 837-934.
16. S. Vaes and L. Vainerman, Extensions of locally compact quantum groups and the bicrossproduct construction, Adv. Math. 175 (2003), 1-101.
17. S. L. Woronowicz, From multiplicative unitaries to quantum groups, Int. J. Math. 7 (1996), 127-149.
18. S. Zakrzewski, Quantum and classical pseudogroups, Comm. Math. Phys. 134 (1990), 347-395.
19. _, Poisson Lie groups and pentagonal transformations, Lett. Math. Phys. 24 (1992), 13-19.