Classification of actions of discrete amenable groups on strongly amenable subfactors of type III$\lambda$

TL;DR

This paper classifies actions of discrete amenable groups on certain type III subfactors using continuous decomposition, establishing a complete invariant that simplifies previous classification results.

Contribution

It removes extra assumptions in prior classifications and provides a comprehensive classification up to cocycle conjugacy using Winsl{ exto}w's fundamental homomorphism.

Findings

Complete classification of group actions on type III$_mbda$ subfactors

Winsl{ exto}w's homomorphism as a complete invariant

Elimination of previous additional assumptions

Abstract

Using the continuous decomposition, we classify strongly free actions of discrete amenable groups on strongly amenable subfactors of type III$_\lambda, 0 < \lambda < 1$. Winsl{\o}w's fundamental homomorphism is a complete invariant. This removes the extra assumptions in the classification theorems of Loi and Winsl{\o}w and gives a complete classification up to cocycle conjugacy.