Classifiable C*-algebras have quantum symmetries

Abstract

We show that every classifiable simple C*-algebra, in particular the Jiang-Su algebra, admits outer actions of several discrete quantum groups, such as finite quantum groups and duals of certain free compact quantum groups. As a consequence of the construction, we provide new examples of hyperfinite subfactors with the Temperley-Lieb-Jones standard invariant and show that ${\mathrm{SU}}_q(2)$ can act minimally on some Araki-Woods factors for infinitely many $q$.

31 pages