Structure of modular invariant subalgebras in free Araki–Woods factors

Boutonnet, Rémi; Houdayer, Cyril

doi:10.2140/apde.2016.9.1989

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Structure of modular invariant subalgebras in free Araki–Woods factors

Rémi Boutonnet and Cyril Houdayer

Vol. 9 (2016), No. 8, 1989–1998

DOI: 10.2140/apde.2016.9.1989

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 quasifree state is necessarily contained in the almost periodic free summand.

Keywords

free Araki–Woods factors, Popa's asymptotic orthogonality property, type III factors, ultraproduct von Neumann algebras

Mathematical Subject Classification 2010

Primary: 46L10, 46L54, 46L36

Milestones

Received: 24 February 2016

Revised: 9 June 2016

Accepted: 3 October 2016

Published: 11 December 2016

Authors

Rémi Boutonnet
Institut de Mathématiques de Bordeaux, CNRS Université Bordeaux I 33405 Talence France

Cyril Houdayer
Laboratoire de Mathématiques d’Orsay Université Paris-Sud, CNRS 91405 Orsay France

Vol. 9, No. 8, 2016