Classification of Roberts actions of strongly amenable C^* tensor categories on the injective factor of type III_1

TL;DR

This paper extends the classification of certain tensor categories by applying Popa's theorem to strongly amenable subfactors of type III_1, broadening the understanding of their realizations in operator algebras.

Contribution

It generalizes Izumi's uniqueness result from type II_1 factors to type III_1 factors for strongly amenable C^*-tensor categories.

Findings

Unified classification framework for strongly amenable C^*-tensor categories on type III_1 factors

Application of Popa's theorem to establish uniqueness of realizations

Extension of previous results from type II_1 to type III_1 factors

Abstract

In this paper, we generalize Izumi's result on uniqueness of realization of finite C$^*$-tensor categories in the endomorphism category of the injective factor of type II_1 for finitely generated strongly amenable C$^*$-tensor categories by applying Popa's classification theorem of strongly amenable subfactors of type III_1.