Centrally free actions of amenable C$^*$-tensor categories on von Neumann algebras

Abstract

We will show a centrally free action of an amenable rigid C$^*$-tensor category on a properly infinite von Neumann algebra has the Rohlin property. This enables us to prove the fullness of the crossed product of a full factor by minimal action of a compact group. As another application of the Rohlin property, we will show the uniqueness of centrally free cocycle actions of an amenable rigid C$^*$-tensor category on properly infinite von Neumann algebras.