On the cocycle bicrossed product construction
Abstract:
The cocycle bicrossed product construction, which involves a matched
pair of groups and a group of 3-cocycles, was proposed for finite groups
by G.I. Kac [1] and is now used for constructing examples of locally compact
quantum groups [2]. A corresponding construction of a Lie bialgebra also
exists for a matched pair of Lie algebras [3].
In the case where the groups in the matched pair are Lie groups, we give a relationship between the groups of differentiable cocycles for the matched pair of groups and the matched pair of the corresponding Lie algebras.