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Answer by Robert Bryant for Why is the automorphism group of the octonions...
The quaternions are generated by any two imaginary elements $x$ and $y$ that are orthonormal, i.e., $\bigl(1,\, x,\, y,\, xy\bigr)$ is an orthonormal basis of the quaternions. Moreover, the...
View ArticleWhy is the automorphism group of the octonions $G_2$ instead of $SO(7)$
I can calculate the derivation of the octonions and I clearly find the 14 generators that form the algebra of $G_2$. However, when I do the same calculation for the quaternions, I end up with the three...
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