This is a survey on some results obtained recently in the classification of compact quantum groups associated to partitions, with a focus on the non-crossing case. We take a global look at the main results in the subject and highlight some key features of the methods used. We conclude by several suggestions for pushing further the classification.

中文翻译：

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关于划分量子群的分类

这是对最近在与分区相关的紧凑量子群的分类中获得的一些结果的调查，重点是非交叉情况。我们全面审视了该主题的主要结果，并强调了所用方法的一些关键特征。我们总结了一些进一步推动分类的建议。