6 problems

Let $D=\mathsf k[h]$ and let $D^*$ be its Harish-Chandra subalgebra. For a maximal ideal $\mathsf m\in\operatorname{SpecMax}D^*$ and an irreducible module…

Let $D$ be a skew-affine generalized Weyl algebra of rank two, meaning that $D=T[t_1,t_2]$ for a finitely generated commutative $\mathbb{C}$-algebra $T$, with automorphisms…

Let $R$ be an affine $\Bbbk$-algebra and let $W:=R(\mathbf x,\mathbf y,\sigma,h)$ be a generalized Weyl algebra of degree $m$. Write … Assume that $R$ is a finitely generated modul…

TGWA birational equivalence conjecture. TGWAs are birationally equivalent to smash products with higher-rank tori.

Let $R=D(\sigma,a)$ be a quantum generalized Weyl algebra, and let $\phi=\eta_{\gamma,\mu}$ be a finite-order diagonal automorphism as in Corollary 1, with…

Let $R=D(\sigma,a)$ be a quantum generalized Weyl algebra, and suppose that finite subgroups of $G=\operatorname{Aut}(R)$ have the forms listed in Proposition 1. If $a$ is symmetri…