Quantizations of some Poisson–Lie groups: The bicrossed product construction

By working with several specific Poisson–Lie groups arising from Heisenberg Lie bialgebras and by carrying out their quantizations, a case is made for a useful but simple method of constructing locally compact quantum groups. The strategy is to analyze and collect enough information from a Poisson–Lie group, and using it to carry out a “cocycle bicrossed product construction”. Constructions are done using multiplicative unitary operators, obtaining C∗C∗-algebraic, locally compact quantum (semi-)groups.