Double crossed products of locally compact quantum groups

Details Double crossed products of locally compact quantum groups Double crossed products of locally compact quantum groups

2002-11-08

arxiv.org/abs/math/0211145v1

Journal of the Institute of Mathematics of Jussieu 4 (2005), 135--173.

Mathematics

Operator Algebras

29 pages, LaTeX

Scientific paper

10.1017/S1474748005000034

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.

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