Integrable Generators of Polynomial Vector Fields for Complex Classical Lie Groups

Source abstract

We consider in this paper complex Lie groups $\mathrm{SL}_n(\mathbb{C})$ for $n\geq 2$, $\mathrm{SO}_n(\mathbb{C})$ for $n\geq 5$, and $\mathrm{Sp}_{2n}(\mathbb{C})$ for $n\geq 1$. We show that for any such Lie group, the Lie algebra of polynomial vector fields can be generated by three $\mathbb{C}$-complete polynomial vector fields.