Subgroups of Quantum Groups

TL;DR

This paper explores the concept of subgroups within quantum groups, proposing a general definition, focusing on reductive cases, and employing categorical methods to deepen understanding of quantum subgroups.

Contribution

It introduces a comprehensive definition of quantum subgroups, especially reductive ones, and reformulates existing results using module and monoidal categories.

Findings

Proposed a unified definition of quantum subgroups.

Characterized reductive quantum subgroups with flatness conditions.

Reformulated quantum subgroup theory in categorical language.

Abstract

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. 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.