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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeDec 12th 2018
    • (edited Dec 12th 2018)

    added pointer to today’s article by Ross Street:

    A general abstract formulation of Rost 96 in terms of string diagrams in additive braided monoidal categories is in

    diff, v21, current

    • CommentRowNumber2.
    • CommentAuthorGuest
    • CommentTimeJan 4th 2021
    The following reported error is stopping this page from loading past the contents for me:

    "error on line 527 at column 6: Opening and ending tag mismatch: div line 0 and ul"

    —Jeff Carlson
    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJan 4th 2021

    Thanks for the alert.

    I have tried to locate the problem. Some experimenting shows that all parts of the entry compile fine by themselves, but something in the second half fails if the TOC is included.

    A smaller (non-)working example is now in the Sandbox. This is essentially the second half of the entry, but with the TOC included. And it still gives the error message.

    The error message in the Sandbox goes away if one makes one of the following two edits:

    1) remove the TOC


    2) after the line

      ### Hurwitz's Theorem 

    add a line

      #### AAAA

    In the latter case one sees that the Theorem (the Hurwitz theorem) appears as a subsection in the TOC. Which is a bug.

    So I am guessing that this is related to the cause of the problem. On the other hand, removing that theorem doesn’t make the error go away either!

    So I give up now.

    • CommentRowNumber4.
    • CommentAuthorRichard Williamson
    • CommentTimeJan 4th 2021
    • (edited Jan 4th 2021)

    Thank you for reporting this, Jeff, I have fixed the page now.

    (For Urs and others, for future reference: since we allowed level 6 headings (i.e. use of ###### in a section heading), the parser has to distinguish theorem environments, which are at the same heading depth HTML-wise, from these. Syntax that it does not expect in a theorem environment can confuse the parser in this respect. In this case, it came from the ’naming’ of the theorem in an old Instiki theorem environment. In general, using the new theorem environment syntax should avoid such issues; I fixed things here by replacing the old theorem syntax with the new. I will tweak the parser when I get the chance to try to handle this kind of case, though, for backwards compatibility.

    As a general rule, for table of contents issues, replacing old Instiki syntax with the new theorem environment syntax should fix things; of course it may not be practical to replace an entire page-worth, but usually there are only a few (if any) theorem environments which are non-standard and which might cause problems.)

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeJan 4th 2021

    Thanks, Richard. I forget about the new syntax. It’s not document in HowTo, is it?

    • CommentRowNumber6.
    • CommentAuthorRichard Williamson
    • CommentTimeJan 4th 2021
    • (edited Jan 4th 2021)

    Yes, it’s documented here, that is, in the section How to organize and write content -> Definition-, Theorem-, Proof- environments. However, the list of available environments is slightly outdated, more are available now. On the other hand, I certainly need to find time to update/replace the instructions on the right when one edits to mention this and other new syntax!

    Edit: updated the list of available environments in the HowTo now.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeJan 4th 2021

    Ah. I did check there but didn’t recognize it. Have tried to make the information more explicit now (here).

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeJun 4th 2022

    added a disclaimer at the very top that the notion here is un-related to composition ring,

    and added a comment in the References-section (here) that the terminology here alludes to “composition of sums of squares”. This would deserve to be expanded on much more, for the moment I added a pointer to section 6 of

    • Olga Taussky, Sums of squares, The American Mathematical Monthly 77 8 (1970) 805-830 [[doi:10.2307/2317016]]

    diff, v26, current

    • CommentRowNumber9.
    • CommentAuthorperezl.alonso
    • CommentTimeOct 4th 2023

    edited definition to include cases that are not unital, and added reference to recent arXiv:2309.17435

    diff, v27, current

    • CommentRowNumber10.
    • CommentAuthorperezl.alonso
    • CommentTimeOct 4th 2023

    This begs the question. How do these para- and non-unital composition algebras relate to statements about supersymmetry? In particular, it seems there should be some nice connection to Berger’s theorem.

  1. added a generalization of composition algebras from the category of vector spaces to any monoidal category


    diff, v29, current

    • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeOct 4th 2023

    Where you define structures “in” some category it may be worthwhile to link to internalization, for explanation of what this means, say via

    • CommentRowNumber13.
    • CommentAuthorDavidRoberts
    • CommentTimeOct 4th 2023

    Added definition of the norm, as it was just used without prior warning

    diff, v32, current

    • CommentRowNumber14.
    • CommentAuthorperezl.alonso
    • CommentTimeNov 2nd 2023

    Before I forget, regarding “para-” and supersymmetry (#10), the answer seems to be along the lines of hep-th/9907046 and work along the lines of Section 4 of 1909.04646.