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Mathematics > Operator Algebras

arXiv:math/0405263 (math)
[Submitted on 13 May 2004]

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

Authors:Byung-Jay Kahng
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Abstract: In this paper, we carry out the ``quantum double construction'' of the specific quantum groups we constructed earlier, namely, the ``quantum Heisenberg group algebra'' (A,\Delta) and its dual, the ``quantum Heisenberg group'' (\hat{A},\hat{\Delta}). Our approach will be by constructing a suitable multiplicative unitary operator. In this way, we are able to retain the C*-algebra framework, and thus able to carry out our construction within the category of locally compact quantum groups. This construction is a kind of a generalized crossed product. To establish that the quantum double we obtain is indeed a locally compact quantum group, we will also discuss the dual of the quantum double and the Haar weights on both of these double objects. Towards the end, we also include a construction of a (quasitriangular) ``quantum universal R-matrix''.
Comments: 33 pages
Subjects: Operator Algebras (math.OA); Quantum Algebra (math.QA)
Cite as: arXiv:math/0405263 [math.OA]
  (or arXiv:math/0405263v1 [math.OA] for this version)
  https://doi.org/10.48550/arXiv.math/0405263

Submission history

From: Byung-Jay Kahng [view email]
[v1] Thu, 13 May 2004 22:11:09 UTC (28 KB)
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