4 problems

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 $A$ 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 $A$ be a noetherian, connected graded domain over ${\Bbbk}$ with $\operatorname{GKdim} A=3$. Its graded quotient ring has the form $Q_{gr}(A)\cong D[t,t^{-1};\alpha]$, where…