Advances in mathematics vol:175 issue:1 pages:1-101
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. (C) 2002 Elsevier Science (USA). All rights reserved.