6 problems

Consider the Lie subalgebra $W(1,1)^+$ with basis … where $\mathbb{N}$ is the set of non-negative integers. Conjecture. For any automorphism $\theta\in\operatorname{Aut}(W(1,1)^+)$…

Let $W_+=t^2\Bbbk[t]\frac{d}{dt}$ be the positive Witt algebra, and let $U(W_+)$ denote its enveloping algebra. Ascending chain condition conjecture. The algebra $U(W_+)$ satisfies…

Let $A_d=\mathbb{C}[t_1^{\pm1},\ldots,t_d^{\pm1}]$, let $\mathcal{W}_d=\operatorname{Der}(A_d)$ be the Witt algebra, and let a weight module mean a $\mathcal{W}_d$-module whose wei…

Let $A_n=\mathbb{C}[x_1,\ldots,x_n]$ and let $W_n=\operatorname{Der} A_n$ be the rank-$n$ Witt algebra. Zhao's Witt algebra conjecture. Every nonzero endomorphism of $W_n$ is an au…

Let $\mathfrak{w}_n$ be the Witt algebra with positive nilpotent subalgebra $\mathfrak{n}_+$, and let $L(\lambda,\mu)$ be the modules constructed in Theorem 91 from parameters sati…

Let $W_n$ be the Witt algebra and let $V$ be a mixed $W_n$-module, meaning that $V$ has both finite-dimensional and infinite-dimensional weight spaces in the same coset of its weig…