Soft and hard liberation of compact Lie groups

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.