I型局部紧量子群的模性质
Modular properties of type I locally compact quantum groups
摘要：
本文主要研究I型局部紧量子群。我们展示了如何与$\mathbb{G}$和$\widehat{\mathbb{G}}$上的Haar积分的模块化理论相关的各种运营商的直接积分的水平上的行为。利用这些结果，我们得到一个网络的影响之间的属性，如单模性或traciality的哈尔积分。我们还详细研究了两个例子：离散量子群$\widehat{\mathrm{SU}_q(2)}$和量子$az+b$群。
英文摘要：
The following paper is devoted to the study of type I locally compact quantum groups. We show how various operators related to the modular theory of the Haar integrals on $\mathbb{G}$ and $\widehat{\mathbb{G}}$ act on the level of direct integrals. Using these results we derive a web of implications between properties such as unimodularity or traciality of the Haar integrals. We also study in detail two examples: discrete quantum group $\widehat{\mathrm{SU}_q(2)}$ and the quantum $az+b$ group.
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