关于量子SU（2）、量子E（2）和扩展量子SU（1，1）之间的对应
On a correspondence between quantum SU(2), quantum E(2) and extended quantum SU(1,1)
摘要：
在以前的论文中，我们证明了如何从局部紧量子群对I型因子的作用中得到一个可能的新的局部紧量子群。在另一篇文章中，我们将这种构造方法应用于量子SU（2）在标准Podles球上的作用，得到了Woronowicz量子E（2）。在本文中，我们将把这种技术应用于量子SU（2）在量子射影平面（其相关的冯诺依曼代数确实是一个I型因子）上的作用。然后在另一边出现的局部紧量子群是扩展的SU（1，1）量子群，如Koelink和Kustermans所构造的。我们还证明了存在一个（非平凡的）量子广群，它的角上有上述三个量子群。
英文摘要：
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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