# Tag Archives: solvable group

## 2 Dimensional Connected Algebraic Groups are Solvable

Conventions: $G$ is an algebraic group over an algebraically closed field $k$ and we identify $G$ with $G(k)$. Consider the algebraic groups $\mathbb{G}_a$ and $\mathbb{G}_m$. They are the only one-dimensional connected groups and they are both solvable. What about two-dimensional connected groups? It turns out that if \$ \mathrm{dim} […]