We show that complex semisimple quantum groups, that is, Drinfeld doubles of $q$-deformations of compact semisimple Lie groups, satisfy a categorical version of the Baum–Connes conjecture with trivial coefficients. Our approach, based on homological algebra in triangulated categories, is compatible with the previously studied deformation picture of the assembly map and allows us to define an assembly map with arbitrary coefficients for these quantum groups.

中文翻译：

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关于复半单量子群的装配图

我们证明了复半单量子群，即紧致半单李群的 $q$-变形的 Drinfeld 双倍满足具有平凡系数的 Baum-Connes 猜想的分类版本。我们的方法基于三角分类中的同调代数，与先前研究的装配图变形图兼容，并允许我们为这些量子群定义具有任意系数的装配图。