Extensions of locally compact quantum groups and the bicrossed product construction

Details Extensions of locally compact quantum groups and the bicrossed product construction Extensions of locally compact quantum groups and the bicrossed product construction

2001-01-16

arxiv.org/abs/math/0101133v2

Advances in Mathematics 175 (1) (2003), 1--101.

Mathematics

Operator Algebras

66 pages, LaTeX. Some references added. Discussion added how examples are deformations of usual groups

Scientific paper

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.

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