Controllability of control systems simple Lie groups and the topology of flag manifolds

Ariane Luzia dos Santos, Luiz A. B. San Martin

Let $S$ be subsemigroup with nonempty interior of a complex simple Lie group $G$. It is proved that $S=G$ if $S$ contains a subgroup $G(\alpha )\approx \mathrm{Sl}(2,\mathbb{C})$ gener…