Classification of actions of discrete amenable groups on strongly amenable subfactors of type III_{𝜆}

Abstract

Using the continuous decomposition, we classify strongly free actions of discrete amenable groups on strongly amenable subfactors of type III λ _\lambda , 0 > λ > 1 0>\lambda >1 . Winsløw’s fundamental homomorphism is a complete invariant. This removes the extra assumptions in the classification theorems of Loi and Winsløw and gives a complete classification up to cocycle conjugacy.