Normal Subgroups, Center and Inner Automorphisms of Compact Quantum Groups

TL;DR

This paper investigates the structure of compact quantum groups by defining inner automorphisms, analyzing normal subgroups, and computing the center, revealing differences from classical group theory.

Contribution

It introduces a new class of automorphisms for compact quantum groups, defines the center, and explores the relation between the center and commutator subgroup.

Findings

Defined a class of inner automorphisms for compact quantum groups

Computed the center for several examples of quantum groups

Discussed differences in the relation between center and commutator subgroup from classical groups

Abstract

We introduce a class of automorphisms of compact quantum groups which may be thought of as inner automorphisms and explore the behaviour of normal subgroups of compact quantum groups under these automorphisms. We also define the notion of center of a compact quantum group and compute the center for several examples. We briefly touch upon the commutator subgroup of a compact quantum group and discuss how its relation with the center can be different from the classical case.