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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 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
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.- Hiroshi Ando and Uffe Haagerup, Ultraproducts of von Neumann algebras, J. Funct. Anal. 266 (2014), no. 12, 6842–6913. MR 3198856, DOI 10.1016/j.jfa.2014.03.013
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