# Tag Archives: borel subgroups

## Highlights in Linear Algebraic Groups 10: G/B is Projective

In Highlights 9 of this series, we showed that for an algebraic group $G$ and a closed subgroup $H\subseteq G$, we can always choose a representation $G\to\rm{GL}(V)$ with a line $L\subseteq V$ whose stabiliser is $H$. In turn, this allows us to identify the quotient $G/H$ with the orbit […]

## Highlights in Linear Algebraic Groups 8: Borel Subgroups I

Borel subgroups are an important type of subgroup that will allow us to gain insight into the mysterious structure of algebraic groups. We shall look at the definition and some basic examples in this post. As usual, algebraic group means some linear algebraic group defined over an algebraically closed field $k$. A Borel subgroup […]