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

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.

28 pages, to appear in Trans. Amer. Math. Soc

References in corpus (2)

• Rohlin Flows on Amalgamated Free Product Factors
• Rohlin flows on von Neumann algebras

Cited by in corpus (1)

• Locally Compact Separable Abelian Group Actions on Factors with the Rohlin Property