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

• Autores: Byung-Jay Kahng
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 32, Nº 4, 2006, págs. 1153-1189
• Idioma: inglés
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• Resumen

  • 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.