Soft and hard liberation of compact Lie groups

TL;DR

This paper explores methods to generate compact Lie groups using free quantum groups and free tori, extending existing techniques to cover more classical groups and tori.

Contribution

It introduces new 'soft' and 'hard' methods for the liberation of compact Lie groups, broadening the scope of previous approaches.

Findings

Soft methods extend 'easy' techniques to groups like SO_N and SU_N

Hard methods partly extend soft methods to real and complex tori

The approaches unify generation techniques for classical groups and tori

Abstract

We investigate the liberation question for the compact Lie groups, by using various "soft" and "hard" methods, based respectively on joint generation with a free quantum group, and joint generation with a free torus. The soft methods extend the "easy" methods, notably by covering groups like $SO_N,SU_N$, and the hard methods partly extend the soft methods, notably by covering the real and complex tori themselves.