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lie groups - Does triality give inner automorphisms of the octonions? - MathOverflow
https://mathoverflow.net/questions/500318/does-triality-give-inner-automorphisms-of-the-octonions
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It's well known that you can construct the octonions using triality. One statement of triality is that $\operatorname{Spin}(8)$ has nontrivial outer automorphisms of order 3. On the other hand, the