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DOUBLE CROSSED PRODUCTS OF LOCALLY COMPACT QUANTUM GROUPS

Published online by Cambridge University Press:  10 February 2005

Saad Baaj  and
Stefaan Vaes
Saad Baaj
Affiliation:
Laboratoire de Mathématiques Pures, Université Blaise Pascal, Bâtiment de Mathématiques, 63177 Aubière Cedex, France (saad.baaj@math.univ-bpclermont.fr)
Stefaan Vaes
Affiliation:
Institut de Mathématiques de Jussieu, Algèbres d’Opérateurs et Représentations, 175, rue du Chevaleret, 75013 Paris, France (vaes@math.jussieu.fr)
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Abstract

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For a matched pair of locally compact quantum groups, we construct the double crossed product as a locally compact quantum group. This construction generalizes Drinfeld’s quantum double construction. We study the modular theory and the $\mathrm{C}^*$-algebraic properties of these double crossed products, as well as several links between double crossed products and bicrossed products. In an appendix, we study the Radon–Nikodym derivative of a weight under a quantum group action (following Yamanouchi) and obtain, as a corollary, a new characterization of closed quantum subgroups.

AMS 2000 Mathematics subject classification: Primary 46L89. Secondary 46L65

Keywords

locally compact quantum groupsmatched pairRadon–Nikodym derivativequantum subgroup
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 4 , Issue 1 , January 2005 , pp. 135 - 173
Copyright
2005 Cambridge University Press

Footnotes

Please note that the DOIs in the printed edition of volume 4 issue 1 contained errors. Correct DOIs for each article in this issue are published here online. We apologise for any inconvenience caused