Double crossed products of locally compact quantum groups

Saad Baaj (1) , Stefaan Vaes (2)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal
2 IMJ - Institut de Mathématiques de Jussieu

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 C*-algebraic properties of these double crossed products and 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.

Domaines: Algèbres d'opérateurs [math.OA]; Algèbres quantiques [math.QA]

Saad Baaj, Stefaan Vaes. Double crossed products of locally compact quantum groups. Journal de l' Institut de Mathématiques de Jussieu, 2005, 4, pp.issue 1. ⟨hal-00012253⟩