  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.

Quantum Algebra