16 problems

Noetherianity conjecture. The universal enveloping algebra

Buchstaber's conjecture. The algebra $H^*(W^+)$ is generated, using some non-trivial Massey products, by its first cohomology $H^1(W^+)$.

Let $\W{-1}$ denote the negative Witt algebra, let $\Ua(\W{-1})$ be its enveloping algebra, and let $A_k$ denote the relevant $k$-th Weyl-algebra target. For each $n$, write…

Let $W$ denote the Witt algebra, and consider the direct sum of three copies $W\oplus W\oplus W$. Rigidity conjecture. Based on the analysis for the direct sum of two Witt algebras…

Let $\W{-1}$ denote the negative Witt algebra, let $W$ denote the Witt algebra, let $\Vir$ denote the Virasoro algebra, and let $A_k$ and $\widetilde A_k$ denote the Weyl-type targ…

Let $X:[0,t_0]\to\cX^{in}$ be a smooth path of inward-pointing vector fields. A path is geometrically exponentiable if there exists an annulus with a framing $h$ satisfying…

Let $\operatorname{Witt}^{in}$ be the cone of inward-pointing vector fields on $S^1$, and let $\cP$ be the set of smooth paths $[0,1]\to\operatorname{Witt}^{in}$. A path is geometr…

Standard Lie identity conjecture. All polynomial identities for $athsf{W}_1$ follow from this standard Lie identity.

Let $W_{geq -1}$ be the Lie algebra of polynomial vector fields on the affine line with degrees at least $-1$, let $\Bbbk$ be the base field, and let $L(f)$ and $L(f,g)$ be the sub…

Let $W$ be the Witt algebra, let $\operatorname{U}(W)$ be its universal enveloping algebra, and let $\pi_\gamma$ be the family of representations defined in the paper, with kernels…

Let $W$ be the Witt algebra and let $\operatorname{U}(W)$ be its universal enveloping algebra. The Witt prime-to-primitive containment conjecture. Every proper prime ideal of…

Let $W$ be the Witt algebra and $W_{\geq -1}$ its subalgebra spanned by the basis elements of index at least $-1$. Let $\operatorname{U}(W)$ and $\operatorname{U}(W_{\geq -1})$ be…

Let $\mathbb K$ be a field of characteristic zero, and let $W_+$ be the positive Witt algebra with basis $\{e_n:n\geqslant 1\}$ and Lie bracket $[e_i,e_j]=(j-i)e_{i+j}$. Its univer…

Let $\mathfrak g=\bigoplus_{k\in\mathbb Z}\mathfrak g_k$ be an infinite-dimensional simple $\mathbb Z$-graded Lie algebra of finite growth, meaning that…

Let $W$ be the Witt algebra and $V$ the Virasoro algebra, with ${\rm U}(W)$ and ${\rm U}(V)$ their universal enveloping algebras. The analogues for ${\rm U}(W)$ and ${\rm U}(V)$ of…

Ext¹-quiver conjecture. This equality should hold for every even $r$ and every $p$.