Not signed in (Sign In)

# Start a new discussion

## Not signed in

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

• Sign in using OpenID

## Discussion Tag Cloud

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

• 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 $Aut(\mathbb{O}) = G_2$.

• 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 $\pm 1$.

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

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

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeApr 24th 2018

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

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeApr 24th 2018

made explicit the definition of real and imaginary octonions here

• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeApr 24th 2018

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

• 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

• CommentRowNumber9.
• CommentAuthorUrs
• CommentTimeApr 25th 2018

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

$L_{e_7} L_{e_6} L_{e_5} L_{e_4} L_{e_3} L_{e_2} L_{e_1} = + 1$
Add your comments
• Please log in or leave your comment as a "guest post". If commenting as a "guest", please include your name in the message as a courtesy. Note: only certain categories allow guest posts.
• To produce a hyperlink to an nLab entry, simply put double square brackets around its name, e.g. [[category]]. To use (La)TeX mathematics in your post, make sure Markdown+Itex is selected below and put your mathematics between dollar signs as usual. Only a subset of the usual TeX math commands are accepted: see here for a list.

• (Help)