Every compact group arises as the outer automorphism group of a II_1 factor

TL;DR

This paper demonstrates that every compact group can be realized as the outer automorphism group of a type II_1 factor, extending previous results from the abelian case using advanced deformation/rigidity techniques.

Contribution

The authors generalize existing methods to show that all compact groups can be realized as outer automorphism groups of type II_1 factors.

Findings

Any compact group can be realized as the outer automorphism group of a type II_1 factor.

Generalization of deformation/rigidity techniques to non-abelian cases.

Extension of previous abelian case results to all compact groups.

Abstract

We show that any compact group can be realized as the outer automorphism group of a factor of type II_1. This has been proved in the abelian case by Ioana, Peterson and Popa applying Popa's deformation/rigidity techniques to amalgamated free product von Neumann algebras. Our methods are a generalization of theirs.