DOUBLE CROSSED PRODUCTS OF LOCALLY COMPACT QUANTUM GROUPS

By Saad Baaj, S. Vaes. Journal of the Institute of Mathematics of Jussieu, 2002

66 citations recorded by the source corpus.

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

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2dc9ad05ce82e3174ab5eed8925d911b49892572

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In Algebra and Number Theory

1. Saad Baaj
2. G. Skandalis
3. S. Vaes
4. K. De Commer
5. A. Furman
6. Adrian Ioana
7. Martijn Caspers
8. Sorin Popa

In Geometry and Topology

1. Saad Baaj
2. G. Skandalis
3. S. Vaes
4. K. De Commer
5. Adrian Ioana
6. T. Banica
7. Damien Gaboriau
8. Martijn Caspers

In Mathematical Physics

1. Saad Baaj
2. S. Vaes
3. G. Skandalis
4. K. De Commer
5. Adrian Ioana
6. Sorin Popa
7. A. Furman
8. Martijn Caspers

Citations in the corpus

• Non-Semi-Regular Quantum Groups Coming from Number Theory (2002, background): “Non-Semi-Regular Quantum Groups 149 Proof. a) This follows from [ 4 ].”