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Rohlin flows on von Neumann algebras

About this Title

Toshihiko Masuda,

Graduate School of Mathematics, Kyushu University, Fukuoka, 819-0395

, Japan

and Reiji Tomatsu,

Department of Mathematics, Hokkaido University, Hokkaido 060-0810

, Japan

Publication: Memoirs of the American Mathematical Society
Publication Year: 2016; Volume 244, Number 1153
ISBNs: 978-1-4704-2016-1 (print); 978-1-4704-3506-6 (online)
DOI: https://doi.org/10.1090/memo/1153
Published electronically: June 21, 2016
Keywords: von Neumann algebra, flow, Rohlin property
MSC: Primary 46L40; Secondary 46L55

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Table of Contents

Chapters

  • 1. Introduction
  • 2. Preliminary
  • 3. Flows on ultraproduct von Neumann algebras
  • 4. Rohlin flows
  • 5. Classification of Rohlin flows
  • 6. Applications
  • 7. Characterization of Rohlin property
  • 8. Concluding remarks and Problems
  • 9. Appendix

Abstract

We will classify Rohlin flows on von Neumann algebras up to strong cocycle conjugacy. This result provides alternative approaches to some preceding results such as Kawahigashi’s classification of flows on the injective type II$_1$ factor, the classification of injective type III factors due to Connes, Krieger and Haagerup and the non-fullness of type III$_0$ factors. Several concrete examples are also studied.

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