Structure of modular invariant subalgebras in free Araki-Woods factors

TL;DR

This paper proves that amenable subalgebras invariant under modular automorphisms in free Araki-Woods factors are contained in the almost periodic summand, clarifying their structural properties.

Contribution

It establishes a structural characterization of invariant amenable subalgebras in free Araki-Woods factors, linking them to the almost periodic summand.

Findings

Amenable invariant subalgebras are contained in the almost periodic summand.

The result applies to subalgebras invariant under the modular automorphism group.

Provides insight into the structure of free Araki-Woods factors.

Abstract

We show that any amenable von Neumann subalgebra of any free Araki-Woods factor that is globally invariant under the modular automorphism group of the free quasi-free state is necessarily contained in the almost periodic free summand.