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arXiv · 1308.2031

A Classification of Flows on AFD Factors with Faithful Connes--Takesaki Modules

Koichi Shimada
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Abstract

We classify flows on AFD factors with faithful Connes-Takesaki modules. This is a generalization of classification of trace-scaling flows on the AFD $\mathrm{II}_\infty$ factor, which is equivalent to the uniqueness of the AFD $\mathrm{III}_1$ factor. In order to do this, we show that a flow on an AFD factor with faithful Connes-Takesaki module has the Rohlin property, which gives a partial answer to a characterization problem of the Rohlin property posed by Masuda-Tomatsu. It is also possible to think of this result as an $\mathbf{R}$-version of Izumi's result about compact group actions on type III factors with faithful Connes-Takesaki modules.

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BibTeXRIS

Koichi Shimada. 2014-05-20. A Classification of Flows on AFD Factors with Faithful Connes--Takesaki Modules. https://arxiv.org/abs/1308.2031

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