Subgroups of quantum groups

Thesis

In this thesis we investigate the notion of a subgroup of a quantum group. We suggest a general definition, which takes into account the work that has been done for quantum homogeneous spaces. We further restrict our attention to reductive subgroups, where some faithful flatness conditions apply. We give examples of quantum subgroups, some known and some new, which are all part of the family of spherical subgroups. The ultimate goal would be to quantize all spherical subgroups. Furthermore, we proceed with a categorical approach to the problem of finding quantum subgroups. We translate all existing results into the language of module and monoidal categories and give another characterization of the notion of a quantum subgroup.

Authors: Christodoulou, G

• DOI: 10.5287/ora-o05npx7nr
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford