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nLab > Latest Changes: Hurwitz theorem

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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeMar 16th 2015

    I am trying to imrpove the complex of entries revolving around the Hurwitz theorem. I am not done yet at all, but since in the process I am touching a lot of entries, I thought I’d drop a note now for those anxiously following the RecentlyRevised notifications.

    So I gave Hurwitz theorem its own entry, first of all, cross linking to the details (a proof,in fact), that may be found at composition algebra, but which previously could not be found from normed division alegbra. Now there are cross-links.

    I also tried to add more references, but this needs work. It seems that Wikipedia says both that the source is

    • Adolf Hurwitz, Über die Composition der quadratischen Formen von beliebig vielen Variabeln, Nachr. Ges. Wiss. Göttingen (1898) 309–316

    as well as that “was published posthumously in 1923”.

    But I haven’t really spent much effort yet to check.

    I also added cross-links with Hopf invariant one, but this is plain stubby for the moment.

    • CommentRowNumber2.
    • CommentAuthorDavidRoberts
    • CommentTimeMar 16th 2015
    • (edited Mar 17th 2015)

    I added a pdf link to the 1898 paper, and a reference and pdf link to the 1923 paper.

    The front of the 1898 paper says

    Ueber die Composition der quadratischen Formen von beliebig vielen Variabein .

    Von

    A . Hurwitz in Zürich , correspondirendem Mitgliede der Gesellschaft . ’

    Vorgelegt in der Sitzung am 9 . Juli 1898 .

    So the result was at least submitted/communicated in 1898. The 1923 paper in Math Annalen says approximately (OCR from GDZ):

    Die vorliegende Arbeit fand sich unter den nachgelassenen Manuskripten von A. Hurwitz und ist hier, abgesehen von der Korrektur einiger unbedeutender Schreib-fehler, üngeändert abgedruckt. Die genaue Prüfung der Arbeit verdanken wir Herrn L. E. Dickson in Chicago, ebenso wie einige Bemerkungen, die hier in deutscher Übersetzung als Fußnoten abgedruckt sind.

    My German is not up to the task, but I’m guessing the proof is in the 1923 paper, though the theorem is in the 1898 paper?

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeMar 17th 2015

    Thanks! Maybe I’ll find the time to check out the original. Thanks again.

    • CommentRowNumber4.
    • CommentAuthorTobyBartels
    • CommentTimeSep 18th 2018

    Fixed misspelt redirects.

    diff, v7, current

    • CommentRowNumber5.
    • CommentAuthorperezl.alonso
    • CommentTimeOct 4th 2023

    generalized hurwitz theorem

    diff, v8, current

  6. changed higher algebra - contents to algebra - contents in context sidebar

    Anonymouse

    diff, v11, current

1 to 6 of 6

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