3 problems

Classification conjectures. (1) Every Hamiltonian operator is equivalent to one whose leading coefficient is $1$. For $N=2n+3\geq 3$, this is equivalent to an operator with leading…

Let $A=\mathbb{C}[D]L\oplus\mathbb{C}[D]W_1\oplus\cdots\oplus\mathbb{C}[D]W_{\ell-1}\oplus\mathbb{C}C$ be a $\mathbb{C}[D]$-module with $DC=0$. Endow $S(A)$ with a Poisson…

Let a non-quasiconstant coefficient Poisson $\lambda$-bracket on $\widetilde{\mathcal{R}}_1$ have odd order $N$ and level $m$, where the level is defined by…