8 problems

Let $A$ be a $\mathcal{J}(\alpha,\beta)$-algebra generated by four primitive axes. Here, $\mathcal{J}(\alpha,\beta)$ denotes the class of algebras under consideration with eigenval…

Projective-group conjecture. There exist parameters $\alpha,\beta,\gamma,\psi\in F$ such that $T\simeq PSL(3,F)$, and a different set of parameters such that $T\simeq PSU(3,F)$. Th…

Classification conjecture. Every algebra of Jordan type is either a Jordan algebra, a Matsuo algebra, or a factor of a Matsuo algebra.

Let $F$ be a field of characteristic different from $2$. Let $J$ be a Jordan algebra over $F$ generated by idempotents, and let a $\mathcal{J}(\frac{1}{2})$-axial central extension…

Let $A$ be a $2$-generated axial algebra of Monster type over a field of characteristic $0$. Sakuma's conjecture. The algebra $A$ is one of the nine Norton–Sakuma algebras. A class…

Let $A$ be an axial algebra of Monster-type with generating axes $X$, and let $\Delta(X)$ be the graph whose vertices are the axes in $X$, with distinct vertices $a,b$ adjacent exa…

Let $A$ be a dihedral axial algebra of Monster type over a field of characteristic $0$. The nine Norton–Sakuma algebras are the nine classified dihedral algebras arising in this se…

Let $A$ be a primitive axial algebra of Monster type, with set of axes and Miyamoto group acting on $A$. Frobenius form conjecture. Every such algebra admits a Frobenius form which…