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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJan 20th 2016
    • (edited Jan 20th 2016)

    Added the definition of “basic triples” of octonions, and the statement that they form a torsor over Aut(𝕆)=G 2Aut(\mathbb{O}) = G_2.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeDec 14th 2016

    added the actual definition to octonions

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeApr 23rd 2018

    added statement and proof (here) that the product of all the seven imaginary quaternions with each other is ±1\pm 1.

    diff, v16, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeApr 23rd 2018
    • (edited Apr 23rd 2018)

    Added a statement (here) concerning projecting out \mathbb{H} from 𝕆\mathbb{O}.

    diff, v17, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeApr 24th 2018

    added statement and proof (here) that the octonions are alternative

    diff, v18, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeApr 24th 2018

    made explicit the definition of real and imaginary octonions here

    diff, v18, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeApr 24th 2018

    stated the Clifford action of the imaginary octonions induced by left multiplication (here)

    diff, v19, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeApr 24th 2018
    • (edited Apr 24th 2018)

    added statement and Clifford-theoretic proof (here) that the consecutive left product by all the seven imaginary generators acts as the identity

    diff, v19, current

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeApr 25th 2018

    Determined the remaining sign ±1\pm 1 in that prop:

    L e 7L e 6L e 5L e 4L e 3L e 2L e 1=+1 L_{e_7} L_{e_6} L_{e_5} L_{e_4} L_{e_3} L_{e_2} L_{e_1} = + 1

    diff, v20, current

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