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

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 I I ∞ \mathrm {II}_\infty , which is equivalent to the uniqueness of the AFD factor of type I I I 1 \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.