论文标题
I型局部紧凑量量子组的模块化特性
Modular properties of type I locally compact quantum groups
论文作者
论文摘要
以下论文致力于研究I型局部紧凑型量子基团的研究。我们展示了与$ \ mathbb {g} $和$ \ wideHat {\ mathbb {g}} $在直接积分级别上行动的各种运算符如何与HAAR积分模块化理论相关。使用这些结果，我们得出了诸如HAAR积分的非模块性或奇特性之类的属性之间的含义。我们还详细研究了两个示例：离散量子组$ \ wideHat {\ mathrm {su} _q（2）} $和量子$ az+b $ group。
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.
