10 problems

Let $A$ be a 3-dimensional Sklyanin algebra, and let $\tau$ be a torsion point of order $n$ on its associated elliptic curve, with $(n,3)=3$. Consider the simple finite-dimensional…

Let $V$ be a $4$-dimensional vector space over $\Bbbk$ with basis $\{x_0,x_1,x_2,x_3\}$. Let $H=\underline{\operatorname{aut}}^l(\Bbbk[x_0,x_1,x_2,x_3])$ and…

Let $A$ be a connected graded domain with $\operatorname{GKdim}(A)=3$, and let … be its graded quotient division ring. Artin's conjecture. One of the following holds: 1. $D$ is fin…

Let $S_{a,b,c}$ be the three-dimensional elliptic Sklyanin algebra associated with the point $\tau=[a:b:c]$ on the elliptic curve $E_{pt}$, and let…

Let $(a,b,c,d)\in\Bbbk^4-\{0\}$, and let $R(a,b,c,d)$ be the algebra generated by $x_1,x_2,x_3,x_4$ subject to relations (R1)–(R6) in the source. The parameters are considered up t…

Let $R$ be a non-PI Sklyanin algebra of dimension at least $3$, and let $G$ be a finite subgroup of $\operatorname{Aut}_{gr}(R)$. Since $R$ has no quasi-reflection of finite order,…

Let $A_v$ be the graded algebra defined by the six quadratic relations in the source, and let $C_1$ and $C_2$ be the two specified elements of $A_v$. The center of $A_v$ is the set…

Let $A_v$ be the graded algebra generated by $x_1,x_2,x_3,x_4$ with the six quadratic relations displayed in the source, and let $C_1=a x_1 x_3+b x_2 x_4+c x_2^2+d x_1^2$ and $C_2$…

For an odd prime $p$, let the $p$-dimensional Sklyanin algebras be the algebras associated to points of order $2$ on an elliptic curve. A graded Clifford algebra is a graded algebr…

Let $E$ be the elliptic curve and let $T(\mathbf{d})$ be the algebra associated to an effective divisor $\mathbf{d}$ on $E$ as in Theorem 9. Let $M$ be a finitely generated $g$-div…