A category equivalence on the Lie algebra of polynomial vector fields

Genqiang Liu, Yufang Zhao

For any positive integer $n$, let $W_n=\text{Der}(\mathbb{C}[t_1,\dots ,t_n])$. The subspaces $\mathfrak{h}_n=\text{Span}\{t_1\frac{\partial}{\partial{t_1}},\dots,t_n\frac{\partial}…