Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Forgot your password?
• Apply for membership

1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeFeb 8th 2013
   • PermaLink
   Author: Urs
   Format: MarkdownItexat _[[Atiyah Lie groupoid]]_ was this old query box discussion, which hereby I am moving from there to here: +-- {: .query} What is all of this $diag$ stuff? I don\'t understand either $(P \times P)/_{diag} G$ or $(P_x \times P_x)_{diag} G$. ---Toby [[David Roberts]]: It's to do with the diagonal action of $G$ on $P\times P$ as opposed to the antidiagonal (if $G$ 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 $P$ as a right $G$-module and the second a left module, where the actions are related by $g p = p g^{-1}$. _Toby_: H\'m, maybe we should write [[diagonal action]] if there\'s something interesting to say about it. =--

   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 $diag$ stuff? I don't understand either $(P \times P)/_{diag} G$ or $(P_x \times P_x)_{diag} G$. —Toby

   David Roberts: It’s to do with the diagonal action of $G$ on $P\times P$ as opposed to the antidiagonal (if $G$ 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 $P$ as a right $G$-module and the second a left module, where the actions are related by $g p = p g^{-1}$.

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

2. • CommentRowNumber2.
   • CommentAuthorDmitri Pavlov
   • CommentTimeJul 27th 2020
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexDiscussion on [[MathOverflow]]: <https://mathoverflow.net/questions/366741/what-is-the-natural-lie-groupoid-structure-on-the-atiyah-lie-groupoid-of-a-princ>

   Discussion on MathOverflow: https://mathoverflow.net/questions/366741/what-is-the-natural-lie-groupoid-structure-on-the-atiyah-lie-groupoid-of-a-princ