7 problems

Let $A$ be an algebra of Jordan type $\frac{1}{2}$. The original conjecture was that $A$ is either a Matsuo algebra, or a factor of a Matsuo algebra, or a Jordan algebra. Desmet's…

McInroy–Shpectorov conjecture. Every connected Jordan type $\eta = \tfrac{1}{2}$ algebra is either a Jordan algebra or a quotient of a Matsuo algebra.

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

Let $\mathbb{F}$ be a field of characteristic not equal to two, and let $A$ be a commutative primitive axial algebra over $\mathbb{F}$ of Jordan type $\frac{1}{2}$, meaning that…

Let $V$ be a simple VOA satisfying the paper's Conditions 1, let $E_V$ be the set of Ising vectors of $V$ of $\sigma$-type, and let $G_V=\langle \sigma_e\mid e\in E_V\rangle$. The…

Let $V$ be a VOA of OZ-type generated by its Ising vectors of $c3$-type, and suppose the associated Matsuo algebra is defined as in the source. A VOA has a compact real form when i…

Very regularity conjecture. Every maximal connected parabolic subgroup $H$ of a connected $3$-transposition group $(G,D)$ is very regular.