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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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A classification of flows on AFD factors with faithful Connes–Takesaki modules
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by Koichi Shimada PDF
Trans. Amer. Math. Soc. 368 (2016), 4497-4523 Request permission

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
  • 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
  • © Copyright 2015 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 368 (2016), 4497-4523
  • MSC (2010): Primary 46L10
  • DOI: https://doi.org/10.1090/tran/6471
  • MathSciNet review: 3453378