On the problem of classifying simple compact quantum groups

TL;DR

This paper reviews simple compact quantum groups, discusses their classification challenges, and demonstrates the simplicity of several newly constructed quantum groups using recent results.

Contribution

It provides a comprehensive review of simple compact quantum groups and proves the simplicity of recent examples using new theoretical results.

Findings

Several new quantum groups are shown to be simple.

The paper discusses the construction and classification problems of simple compact quantum groups.

Abstract

We review the notion of simple compact quantum groups and examples, and discuss the problem of construction and classification of simple compact quantum groups. Several new quantum groups constructed by Banica, Curran and Speicher since the author's first paper on simple quantum groups are shown to be simple using results of Raum and Weber.