AIMS Lie Groups: Fall-2022 Practice Exercises 13 : Due 13 Wed 21 Dec
Automorphisms of $\mathbb{O}$
S0 4495S
Find an automorphism of the octonions \(\mathbb{O}\). That is, find a map \(\Phi:\mathbb{O}\longmapsto\mathbb{O}\) satisfying
\[
\Phi(xy)=\Phi(x)\Phi(y) .
\]
HINT: It is enough to consider maps that take basis elements to other basis elements (up to sign).