Non-classification of free Araki-Woods factors and τ-invariants

Román Sasyk; Asger Törnquist; Stefaan Vaes

doi:10.4171/GGD/520

Non-classification of free Araki-Woods factors and τ-invariants

Román Sasyk, Asger Törnquist, Stefaan Vaes

Department of Mathematical Sciences

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Abstract

We define the standard Borel space of free Araki-Woods factors and prove that their isomorphism relation is not classifiable by countable structures. We also prove that equality of τ-topologies, arising as invariants of type III factors, as well as cocycle and outer conjugacy of actions of abelian groups on free product factors are not classifiable by countable structures.

Original language	English
Journal	Groups, Geometry, and Dynamics
Volume	13
Issue number	4
Pages (from-to)	1219-1234
ISSN	1661-7207
DOIs	https://doi.org/10.4171/GGD/520
Publication status	Published - 2019

Keywords

Classification of factors and their automorphisms
Descriptive set theory
Fourier analysis on locally compact abelian groups
Von Neumann algebras

Access to Document

10.4171/GGD/520

OA-Non-classification of free Araki-Woods factors and τ -invariantsAccepted author manuscript, 188 KBLicence: Unspecified

Cite this

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AU - Vaes, Stefaan

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KW - Descriptive set theory

KW - Fourier analysis on locally compact abelian groups

KW - Von Neumann algebras

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