11 problems

Let $F$ be a field of zero characteristic, and let $J$ be a simple Jordan superalgebra over $F$ with nonzero odd part. The possible superalgebras include $H(A,*)$, where $(A,*)$ is…

Poisson $n$-Lie algebra construction conjecture. Then $(\mathcal A, \cdot, [-,\dots,-])$ forms a Poisson $n$-Lie algebra.

Commutative loop conjecture. The structure $(3^{A},\oplus)$ satisfies:

Let $\mathcal{L}=(\{1,a,b,c,d\},\ast)$ be the smallest loop that is not a group, with multiplication operation $\ast$. Loop-switch strategy conjecture. There exists a nontrivial ad…

A gyrogroup is a set equipped with a binary operation and the associated gyroautomorphisms satisfying the gyrogroup axioms; it is commutative when its binary operation satisfies…

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

Generalized Kaplansky conjecture. The evaluation of any multilinear polynomial over $A$ is a vector subspace of $A$.

Doro's conjecture. If $\operatorname{Nuc}(M)=1$, then $\operatorname{C}(M)$ is normal in $M$.

Minimal dimension conjecture. Every Malcev algebra of the second type of dimension $<23$ over a field of characteristic $0$ is an algebra of the first type.

The Main Conjecture. The quotient $Q/N(Q)$ is an abelian group and $Q/Z(Q)$ is a group. In particular, $Q$ is nilpotent of class at most $3$.

Let $A_{p,q}$ ($p \le q$) be the simple associative triple system consisting of $(p+q) \times (p+q)$ block matrices of the form … Let $\omega$ be one of the following trilinear ope…