论文标题
紧凑型量子组的傅立叶截断和有限生成的组的收敛性
Convergence of Fourier truncations for compact quantum groups and finitely generated groups
论文作者
论文摘要
我们将Connes和Van Suijlekom定义的Fejér-Riesz运算符系统概括为紧凑型矩阵量子组的设置及其对C*-Algebras的Ergodic作用。这些截断形成了含有C*-Algebra的过滤。我们表明，当它们和包含C*-Algebra配备合适的量子指标时，在合适的条件下，它们会收敛到包含C*-Algebra的量子Gromov-Hausdorff距离。在其他示例中，我们的结果适用于量子组$ su_q（2）$及其同质空间$ s^2_q $。
We generalize the Fejér-Riesz operator systems defined for the circle group by Connes and van Suijlekom to the setting of compact matrix quantum groups and their ergodic actions on C*-algebras. These truncations form filtrations of the containing C*-algebra. We show that when they and the containing C*-algebra are equipped with suitable quantum metrics, then under suitable conditions they converge to the containing C*-algebra for quantum Gromov-Hausdorff distance. Among other examples, our results are applicable to the quantum groups $SU_q(2)$ and their homogeneous spaces $S^2_q$.
