CLASSIFICATION OF ACTIONS OF DISCRETE AMENABLE GROUPS ON AMENABLE SUBFACTORS OF TYPE II

Abstract

We prove a classification result for properly outer actions σ of discrete amenable groups G on strongly amenable subfactors of type II, N ⊂ M, a class of subfactors that were shown to be completely classified by their standard invariant [Formula: see text], in [27]. The result shows that the action σ is completely classified in terms of the action it induces on [Formula: see text]. As an application of this, we obtain that inclusions of type III λ factors, 0 < λ < 1, having discrete decomposition and strongly amenable graph, are completely classified by their standard invariant.