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$_λ, 0 < λ< 1$. Winsløw&#39;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.