Braided quantum groups related to the quantum "ax+b" group

Details Braided quantum groups related to the quantum "ax+b" group Braided quantum groups related to the quantum "ax+b" group

2000-12-30

arxiv.org/abs/math/0101003v2

Mathematics

Quantum Algebra

31 pages LaTeX, no figures

Scientific paper

We consider quantum group theory on the Hilbert space level. We find all unitary representations of three braided quantum groups related to the quantum ``ax+b'' group. First we introduce an auxiliary braided quantum group, which is apparently not related to the quantum ``ax+b'' group, but easy to work with. We find all unitary representations of this quantum group. Then we use this result to find all unitary representations of another braided quantum group, whose C*-algebra is generated by two (out of three) generators generating (in the sense of Woronowicz) C*-algebra of the quantum ``ax+b''- group. We find all unitary representations of this other braided quantum group. This is the most difficult result needed to classify all unitary representations of the quantum ``ax+b'' group.

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