16 problems

Variable-size eigenvector decomposition conjecture. For any $3\times3$ octonionic Hermitian matrix, the associativity relation should hold when suitably rewritten for a set consist…

Generalized orthogonality conjecture. The correct notion of orthogonality is $\operatorname{NewOrtho}$, rather than $\operatorname{Ortho}$.

Musès's conjecture. A simpler version of Dirac's equation using only the 16-dimensional $M$-algebra, namely the complex octonions, is possible.

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.…

Minimal generation conjecture. In case $\mathop{char}\mathbb{F}=2$, the algebra $T_{0,n}$ is minimally generated by

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

Let $G$ be a compact subset of the unit octonions, and consider the lattice gauge theory and its prelinearized version on a polygon triangulated by regular triangles. For $G=SU(2)$…

A tight projective $5$-design in $\mathbb{OP}^2$ is the unique system of $819$ points corresponding to the lines of the generalized hexagon $\mathrm{GH}(2,8)$, and it exhibits…

Affirmative-solutions conjecture. Questions 1, 2, 3 and 4 should have substantially affirmative, possibly demanding, solutions.

Finite-generation conjecture. The known identities of degree $\leq 6$ generate all polynomial identities of $\mathbb{O}$.

Let $L$ be the Moufang loop constructed in the source, and let octonion algebras be the algebras whose norm-one unit loops are Moufang. Moufang-loop and octonion-algebra conjecture…

Let $\mathfrak{R^t}$ be the three-coloured random graph with colour-triality action, and consider the associated triality phenomena for the Leech lattice, Moufang loops, octonion a…

Let $C$ be a fixed constant and let $d$ be an integer with $d>C$. Let $\gamma_d$ denote the supremal asymptotic girth constant for explicit families of $d+1$-regular graphs. An exp…

Let $J_\lambda$ be local almost complex structures on a Riemannian manifold with a $Spin(7)$-structure, determined by … where $P$ is the $Spin(7)$ cross product and the indices ran…

Let $u\in {\mathcal{C}}\ell_{0,7}$ and let $A,B\in\mathbb{O}$, where $\mathbb{O}$ is the octonion algebra. Write $\bullet_\llcorner$ and $\bullet_\lrcorner$ for the corresponding l…