Resumen de Quantum double construction in the C*-algebra setting of certain Heisenberg-type quantum groups

Byung-Jay Kahng

• We carry out the ``quantum double construction'' of the specific quantum groups we constructed earlier, namely, the ``quantum Heisenberg group algebra'' and its dual, the ``quantum Heisenberg group''. Our approach is by constructing a suitable multiplicative unitary operator, retaining the C*-algebra framework of locally compact quantum groups. We also discuss the dual of the quantum double and the Haar weights on both of these double objects. Towards the end, a construction of a (quasitriangular) quantum universal R-matrix is given.