Centrally Free Actions of Amenable C -Tensor Categories on von Neumann Algebras

Reiji Tomatsu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We will show a centrally free action of an amenable rigid C -tensor category on a properly infinite von Neumann algebra has the Rohlin property. Our main result is the classification of centrally free cocycle actions of an amenable rigid C -tensor category up to approximate inner conjugacy on properly infinite von Neumann algebras. This is regarded as a generalization of classification of amenable discrete groups due to A. Connes, V. Jones and A. Ocneanu. We have the following two applications: a classification of centrally free actions of amenable discrete quantum groups of Kac type on von Neumann algebras and another proof of S. Popa’s celebrated classification result of amenable subfactors. As another application of the Rohlin property, we will prove the fullness of the crossed product of a full factor by a minimal action of a compact group.

Original languageEnglish
Pages (from-to)71-152
Number of pages82
JournalCommunications in Mathematical Physics
Volume383
Issue number1
DOIs
Publication statusPublished - 2021 Apr

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Fingerprint

Dive into the research topics of 'Centrally Free Actions of Amenable C <sup>∗</sup> -Tensor Categories on von Neumann Algebras'. Together they form a unique fingerprint.

Cite this