Construction of a quantum Heisenberg group

Details Construction of a quantum Heisenberg group Construction of a quantum Heisenberg group

2003-07-09

arxiv.org/abs/math/0307126v2

Mathematics

Operator Algebras

22 pages

Scientific paper

In this paper, we give a construction of a (C*-algebraic) quantum Heisenberg group. This is done by viewing it as the dual quantum group of the specific non-compact quantum group (A,\Delta) constructed earlier by the author. Our definition of the quantum Heisenberg group is different from the one considered earlier by Van Daele. To establish our object of study as a locally compact quantum group, we also give a discussion on its Haar weight, which is no longer a trace. In the latter part of the paper, we give some additional discussion on the duality mentioned above.

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