3 problems

Let $\mathbb O$ be the octonion algebra, viewed as an $8$-dimensional real algebra, and let $T_{\mathbb O}\in\mathbb R^8\otimes\mathbb R^8\otimes\mathbb R^8$ be its multiplication…

Let $O$ be a split-octonion algebra, and let $f:O\rightarrow O$ be an additive map. Write $O^\times$ for the set of invertible elements of $O$. Split-octonion extension conjecture.…

Octonion image conjecture. The image of this evaluation is a real vector subspace of $\mathbb{O}$.