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Transactions of the American Mathematical Society

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A classification of flows on AFD factors with faithful Connes-Takesaki modules


Author: Koichi Shimada
Journal: Trans. Amer. Math. Soc. 368 (2016), 4497-4523
MSC (2010): Primary 46L10
DOI: https://doi.org/10.1090/tran/6471
Published electronically: October 14, 2015
MathSciNet review: 3453378
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Abstract: We completely classify flows on approximately finite dimensional (AFD) factors with faithful Connes-Takesaki modules up to cocycle conjugacy. This is a generalization of the uniqueness of the trace-scaling flow on the AFD factor of type $ \mathrm {II}_\infty $, which is equivalent to the uniqueness of the AFD factor of type $ \mathrm {III}_1$. In order to achieve this, we show that a flow on any AFD factor with faithful Connes-Takesaki module has the Rohlin property, which is a kind of outerness for flows introduced by Kishimoto and Kawamuro.


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Additional Information

Koichi Shimada
Affiliation: Department of Mathematical Sciences, University of Tokyo, Komaba, Tokyo, 153-8914, Japan
Email: shimada@ms.u-tokyo.ac.jp

DOI: https://doi.org/10.1090/tran/6471
Received by editor(s): August 9, 2013
Received by editor(s) in revised form: February 23, 2014, April 11, 2014, and May 9, 2014
Published electronically: October 14, 2015
Article copyright: © Copyright 2015 American Mathematical Society

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