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Apr 7, 2022 at 12:11 comment added Andromeda @StefaanVaes Thanks for your answer! I don't think that modular automorphism groups are already introduced at this point in Takesaki's book.
Apr 7, 2022 at 12:05 comment added Stefaan Vaes @MaoWao. Yes, of course, but the whole point here is that $\omega$ is not faithful.
Apr 7, 2022 at 11:10 history answered Stefaan Vaes CC BY-SA 4.0