Hostname: page-component-745bb68f8f-mzp66 Total loading time: 0 Render date: 2025-02-11T17:35:50.006Z Has data issue: false hasContentIssue false
  • English
  • Français

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 ([email protected])
Stefaan Vaes
Affiliation:
Institut de Mathématiques de Jussieu, Algèbres d’Opérateurs et Représentations, 175, rue du Chevaleret, 75013 Paris, France ([email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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