Discrete quantum subgroups of complex semisimple quantum groups

2023/03/26 by Kitamura, Kan
#46L67 #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2303.14656

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.

Related

• On certain invariants of compact quantum groups
• The full classification of orthogonal easy quantum groups
• Discrete quantum subgroups of free unitary quantum groups
• On some low dimensional quantum groups
• Discrete quantum group coaction on the circle