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Results tagged with octonions
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user 65801
Octonions form a 8-dimensional normed division algebra constructed over the reals. They can be seen as a non-associative (alternative) extension of the quaternions. They have been first defined and studied in the 19th century by John Graves and Arthur Cayley. There are several variants (such as split-octonions) and strong relations with Lie Groups and projective geometry.
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Why, conceptually, does the torus normalizer in $G_2$ split?
While the following might not be conceptual, but at least it's simple if one knows group cohomology. The obstruction to splitting lives in $H^2(W;T)$, and we have $H^n(W;T)=0$ for all $n\geq 0$!
One w …
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