Factors of type II_1 without non-trivial finite index subfactors

TL;DR

This paper demonstrates the existence of type II_1 factors that lack non-trivial finite index subfactors, showing a new class of factors with highly restricted bimodule structures, building on recent advances in the field.

Contribution

It proves the existence of type II_1 factors with no non-trivial finite index subfactors, extending understanding of subfactor theory and bimodule structures.

Findings

Existence of type II_1 factors without non-trivial finite index subfactors

Every finite coupling constant bimodule is a multiple of L^2(M)

Builds on recent work on type II_1 factors without outer automorphisms

Abstract

We call a subfactor trivial if it is isomorphic with the obvious inclusion of N into matrices over N. We prove the existence of type II_1 factors M without non-trivial finite index subfactors. Equivalently, every M-M-bimodule with finite coupling constant, both as a left and as a right M-module, is a multiple of L^2(M). Our results rely on the recent work of Ioana, Peterson and Popa, who proved the existence of type II_1 factors without outer automorphisms.