22 problems

Let $\tilde{\mathfrak M}$ be the rock-paper-scissors algebra with unit over a field $\mathbb F$, and let $p$ be a homogeneous polynomial in one variable whose sum of coefficients i…

Let $V$ be a simple Lie triple system and let $U(V)$ be its universal enveloping algebra. The augmentation-ideal conjecture. The only proper ideal of $U(V)$ is its augmentation ide…

Let $\mathcal{E}$ be a complex evolution algebra. An element $u\in\mathcal{E}$ is an idempotent if $u^2=u$. If $\mathcal{E}$ has natural basis $\{e_1,\dots,e_n\}$ and structure mat…

Identity-generation conjecture. Every multilinear identity in the mutation of a $\mathfrak{perm}$ algebra over a field of characteristic zero is a consequence of

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…

Ternary multiplication nilpotence conjecture. The associative algebras $L(A)$ and $R(A)$ are nilpotent; in both cases, the nilpotence is of index $13$ and is not less in general.

7-Engel conjecture. The identity $t_4=0$ implies the $7$-Engel identity.

Symmetric weak nilpotence conjecture. The identity $t_4=0$ does not imply $t_5=0$, and hence does not imply the index-$4$ weak nil property; the identities $t_4=t_5=0$ imply the we…

Nilpotence-index-15 conjecture. The associative algebras $L(A)$ and $R(A)$ are nilpotent; in both cases, the nilpotence is of index $15$ and is not less in general.

Binary weak nilpotence conjecture. For each $n$, the identities $w_n=w_{n+1}=\cdots=w_{2n-3}=0$ imply the identity $w_{2n-2}=0$, and hence imply weak nilpotence of index $n$.

Speciality conjecture. Every transposed Poisson algebra is special.

Let $\mathbf{k}$ be the ground field, let $n\geq 1$, and let $\nu_n(\alpha)$ be the $n$-dimensional terminal algebra … For an algebra $A$, write $O(A)$ for its orbit under the rele…

Let $C$ be a finite-dimensional comtrans algebra, without assuming that it is special, and let $U(C)$ denote its enveloping algebra. Finite-dimensionality conjecture. If $C$ is fin…

Let $\mathcal{CT}$ be the symmetric weight-graded comtrans operad, and let $\mathcal{CT}(w)$ denote its component of weight $w$. In the free comtrans algebra, the multilinear subsp…

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…

Let $A$ be a generic algebra, and let $\Pi$ be a $k$-dimensional affine subspace of $A$. An idempotent is an element $e\in A$ satisfying $e^2=e$. The idempotent bound. The affine s…

Local-derivation conjecture. The category of local derivations of $A$ coincides with the category of derivations of $A$.

Bremner–Felipe–Sánchez-Ortega conjecture. If $\mathbb{F}$ has characteristic $0$ or $p>d$, then

Let the simple $7$-dimensional Malcev algebra be the algebra under consideration, and let the Filippov $h$-polynomial be the degree-$5$ polynomial identity associated with it. Fili…

KP–BSO compatibility conjecture. If the field $\mathbb{F}$ has characteristic $0$ or $p>d$, then

Let $FRC_n$ be the multilinear subspace of degree $n$ in the free right-commutative algebra on $n$ generators. An ordered basis of $FRC_n$ consists of the distinct right-commutativ…