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

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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.## References

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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