Discrete Quantum Subgroups of Complex Semisimple Quantum Groups

Abstract

Abstract 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.