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.

1. G.I. Kac, Extensions of groups to ring groups, Math. USSR Sbornik, 1968, v.5, pp. 451-474.
2. S. Vaes and L. Vainerman, Extensions of locally compact quantum groups and the bicrossed product construction, Adv. in Math., 2003. v.175, pp.1-101.
3. A. Masuoka,  Extensions of Hopf Algebras and Lie Bialgebras, Trans. of the AMS, 2000, v.352, n.8, pp.2837-3879.