# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1903.06382