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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeOct 31st 2019

    added pointer to today’s

    diff, v13, current

    • CommentRowNumber2.
    • CommentAuthorDmitri Pavlov
    • CommentTimeJul 28th 2021

    Added:


    nPOV definition

    The modern approach to defining the modular automorphism group is through the theory of noncommutative L_p-spaces. This was pioneered by Haagerup in 1979 \cite{Haagerup} and Yamagami in 1992 \cite{Yamagami}.

    In this approach, given a von Neumann algebra MM, a faithful semifinite normal weight μ\mu on MM, and an imaginary number tt, the modular automorphism associated to MM, μ\mu, and tt is

    σ μ t:MM,mμ tmμ t.\sigma_\mu^t\colon M\to M,\qquad m\mapsto \mu^t m \mu^{-t}.

    This approach makes it easy to deduce various properties of the modular automorphism group.

    For more details, see a MathOverflow answer.


    diff, v16, current

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