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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeDec 18th 2014

    Added to Klein geometry a section History with quotations for where exactly Klein actually speaks about G/HG/H.

    (This key passages is a bit hidden in Klein’s text, appearing at a somewhat unexpected point somewhere in the middle of a 35 page document.)

  1. Iso(d,1)Iso(d,1) contains parity-reversal and time-reversal. To obtain d+1\mathbb{R}^{d+1} from a quotient of Iso(d,1)Iso(d,1), we must quotient these out. Therefore the stabilizer subgroup HH is O(d,1)O(d,1) rather than SO(d,1)SO(d,1).


    diff, v12, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeMar 3rd 2019

    thanks for catching. It was, luckily, correct in the table right below that erroneous line.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeApr 11th 2021

    I have added the publication data and the DOI for the German original, and the projeceuclid-link for the English translation of:

    will give this its own category:reference-page now

    diff, v13, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeJun 14th 2022

    I have added a brief example (here) mentioning that the usual study of crystallography through crystallographic symmetry groups is much in the spirit of Klein geometry (even though I have not yet seen an author admitting this).

    diff, v15, current

    • CommentRowNumber6.
    • CommentAuthorperezl.alonso
    • CommentTimeNov 7th 2023
    • (edited Nov 7th 2023)

    We need some disambiguation, as nowadays many papers take Kleinian geometry to mean geometry modeled over d,d\mathbb{R}^{d,d}.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeNov 8th 2023

    I started a disambiguation here

    (But please feel invited to do such things yourself!)

    diff, v18, current

    • CommentRowNumber8.
    • CommentAuthorperezl.alonso
    • CommentTimeNov 8th 2023

    Thanks, Urs, I actually meant that comment as a note to myself since I had to go take care of something else. I’ll go ahead and create a separate page for this, as I’m planning on adding a couple of related references soon.