On a correspondence between quantum SU(2), quantum E(2) and extended quantum SU(1,1)

Details On a correspondence between quantum SU(2), quantum E(2) and extended quantum SU(1,1) On a correspondence between quantum SU(2), quantum E(2) and extended quantum SU(1,1)

2010-04-24

arxiv.org/abs/1004.4307v1

Mathematics

Quantum Algebra

35 pages

Scientific paper

In a previous paper, we showed how one can obtain from the action of a locally compact quantum group on a type I-factor a possibly new locally compact quantum group. In another paper, we applied this construction method to the action of quantum SU(2) on the standard Podles sphere to obtain Woronowicz' quantum E(2). In this paper, we will apply this technique to the action of quantum SU(2) on the quantum projective plane (whose associated von Neumann algebra is indeed a type I-factor). The locally compact quantum group which then comes out at the other side turns out to be the extended SU(1,1) quantum group, as constructed by Koelink and Kustermans. We also show that there exists a (non-trivial) quantum groupoid which has at its corners (the duals of) the three quantum groups mentioned above.

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