A rigid hyperfinite type $\mathrm{II}_1$ factor

TL;DR

This paper demonstrates the relative consistency of a hyperfinite type II_1 factor with specific properties, including non-isomorphism to its opposite and trivial automorphism group, within set theory.

Contribution

It constructs a hyperfinite type II_1 factor with unique properties that challenge previous assumptions about automorphisms and isomorphisms.

Findings

Existence of a hyperfinite type II_1 factor not isomorphic to its opposite

The factor has no outer automorphisms

It has a trivial fundamental group

Abstract

We show that it is relatively consistent with ZFC that there exists a hyperfinite type $\mathrm{II}_1$-factor of density character $\aleph_1$ which is not isomorphic to its opposite, does not have any outer automorphisms, and has trivial fundamental group.