Extensions of locally compact quantum groups and the bicrossed product construction

2001/01/31 by Stefaan Vaes, Leonid Vainerman
Mathematics · #math.OA #math.QA

paper · pdf

published as Advances in Mathematics 175 (1) (2003), 1--101. · 66 pages, LaTeX. Some references added. Discussion added how examples are deformations of usual groups

arxiv created 2001/03/07 · arxiv updated 2009/11/30

Abstract

In the framework of locally compact quantum groups, we study cocycle actions. We develop the cocycle bicrossed product construction, starting from a matched pair of locally compact quantum groups. We define exact sequences and establish a one-to-one correspondence between cocycle bicrossed products and cleft extensions. In this way, we obtain new examples of locally compact quantum groups.

Related

• The bicrossed product construction for locally compact quantum groups
• Examples of locally compact quantum groups through the bicrossed product construction
• On Low-Dimensional Locally Compact Quantum Groups
• DOUBLE CROSSED PRODUCTS OF LOCALLY COMPACT QUANTUM GROUPS
• On compact bicrossed products