The book contains seven refereed research papers on locally compact quantum groups and groupoids by leading experts in the respective fields. These contributions are based on talks presented on the occasion of the meeting between mathematicians and theoretical physicists held in Strasbourg from February 21 to February 23, 2002. Topics covered are: various constructions of locally compact quantum groups and their multiplicative unitaries; duality theory for locally compact quantum groups; combinatorial quantization of flat connections associated with SL(2,c); quantum groupoids, especially coming from Depth 2 Extensions of von Neumann algebras, C*-algebras and Rings. Many mathematical results are motivated by problems in theoretical physics. Historical remarks set the results presented in perspective. Directed at research mathematicians and theoretical physicists as well as graduate students, the volume will give an overview of a field of research in which great progress has been achieved in the last few years, with new ties to many other areas of mathematics and physics.
Introduction · M. Enock: Quantum groupoids and pseudo-multiplicative unitaries · E. Koelink and J. Kustermans: Quantum SU(1,1) and its Pontryagin dual · P. Schauenburg: Morita base change in quantum groupoids · K. Szlachanyi: Galois actions by finite quantum groupoids · S. Vaes and L. Vainerman: On Low-Dimensional Locally Compact Quantum Groups · J.-M. Vallin: Multiplicative partial isometries and finite quantum groupoids · A. Van Daele: Mulitplier Hopf *-algebras with positive integrals: A laboratory for locally compact quantum groups