Free unitary groups are (almost) simple

TL;DR

This paper proves that certain quotients of universal quantum groups are simple, meaning they lack non-trivial normal quantum subgroups, and are among the first examples of simple compact quantum groups with non-commutative fusion rings.

Contribution

It establishes the simplicity of quotients of universal quantum groups, introducing new examples of simple compact quantum groups with non-commutative fusion rings.

Findings

Quotients of Wang and Van Daele's quantum groups are simple.

First examples of simple compact quantum groups with non-commutative fusion rings.

No normal quantum subgroups in these quotients.

Abstract

We show that the quotients of Wang and Van Daele's universal quantum groups by their centers are simple in the sense that they have no normal quantum subgroups, thus providing the first examples of simple compact quantum groups with non-commutative fusion rings.