DOUBLE CROSSED PRODUCTS OF LOCALLY COMPACT QUANTUM GROUPS

2002/11/08 by Saad Baaj, Stefaan Vaes · 5 citations
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #math.OA #math.QA

paper · pdf · doi:10.1017/s1474748005000034

published as Journal of the Institute of Mathematics of Jussieu 4 (2005), 135--173. · 29 pages, LaTeX

arxiv created 2002/11/08 · openalex publication_date 2005/01/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 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

Cited by

• Equivariant Eilenberg-Watts theorems for locally compact quantum groups
• Quantum double construction in the C*-algebra setting of certain Heisenberg-type quantum groups
• Complex semisimple quantum groups and representation theory
• The standard construction for cocycle twisted and braided tensor product W^*-algebras
• Fundamental isomorphism theorems for quantum groups

Related

• Examples of locally compact quantum groups through the bicrossed product construction
• The bicrossed product construction for locally compact quantum groups
• Extensions of locally compact quantum groups and the bicrossed product construction
• On compact bicrossed products
• Quantum groups with projection on von Neumann algebra level