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

Locally Compact Separable Abelian Group Actions on Factors with the Rokhlin Property

“…Proof. The proof is the same as that of Case ker = 0 of Lemma 6 of [24]. In the proof of Lemma 6 of [24], we use Rohlin's lemma for actions of R 2 .…”

“…The proof is the same as that of Case ker = 0 of Lemma 6 of [24]. In the proof of Lemma 6 of [24], we use Rohlin's lemma for actions of R 2 . Rohlin's lemma for actions of G × R also holds, which is shown by the same argument as in Lemma of Lind [16] and Theorem 1 of [6].…”

“…There exist "many" Rohlin actions on AFD factors of type III 0 . The following is a generalization of a part of [24].…”

“…Example 15. (See Theorem 5 of [24]) Let α be an action of a locally compact abelian group G on an AFD factor M and (θ, Z) be the flow of weights of M . Assume that an action {mod(α g ) • θ t } (g,t)∈G×R of G × R is faithful.…”