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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeFeb 8th 2013

    at Atiyah Lie groupoid was this old query box discussion, which hereby I am moving from there to here:

    +– {: .query} What is all of this diagdiag stuff? I don't understand either (P×P)/ diagG(P \times P)/_{diag} G or (P x×P x) diagG(P_x \times P_x)_{diag} G. —Toby

    David Roberts: It’s to do with the diagonal action of GG on P×PP\times P as opposed to the antidiagonal (if GG is abelian) or the action on only one factor. I agree that it’s a bad notation.

    Toby: How well do you think it works now, with the notation suppressed and a note added in words? (For what it's worth, the diagonal action seems to me the only obvious thing to do here, although admittedly the others that you mention do exist.)

    Todd: I personally believe it works well. A small note is that this construction can also be regarded as a tensor product, regarding the first factor PP as a right GG-module and the second a left module, where the actions are related by gp=pg 1g p = p g^{-1}.

    Toby: H'm, maybe we should write diagonal action if there's something interesting to say about it. =–

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