Rohlin Flows on Amalgamated Free Product Factors

We construct flows on an amalgamated free product factor and characterize the Rohlin property for them by faithfulness of R×Z actions on a measured space. As a corollary, we find Rohlin flows on this factor. This is the first example of Rohlin flows on non-McDuff factors. We also apply Masuda–Tomatsu’s theorem to our Rohlin flows, and obtain a classification up to strong cocycle conjugacy. However, it also turns out that usual cocycle conjugacy is different from strong cocycle conjugacy for our flows. Consequently, even though Masuda–Tomatsu’s analysis is applicable for flows on non-McDuff factors, the effect of their analysis on classification up to cocycle conjugacy is limited.