An analogue of Connes-Haagerup approach for classification of subfactors of type III₁

Abstract

Popa proved that strongly amenable subfactors of type III_1 with the same type II and type III principal graphs are completely classified by their standard invariants. In this paper, we present a different proof of this classification theorem based on Connes and Haagerup's arguments on the uniqueness of the injective factor of type III_1.