Discrete Quantum Subgroups of Complex Semisimple Quantum Groups.

We classify discrete quantum subgroups in the quantum double of the |$q$| -deformation of a compact semisimple Lie group, regarded as the complexification. We also record their classifications in some variants of quantum groups. Along the way, we show that quantum doubles of non-Kac-type compact quantum groups do not admit the quantum analog of lattices considered by Brannan–Chirvasitu–Viselter. [ABSTRACT FROM AUTHOR]