# Tag Archives: reductive group

## Highlights in Linear Algebraic Groups 13: Centralisers of Tori

In Highlights 12, we used some of the equivalent conditions for a connected algebraic group $G$ over a field $k=\overline{k}$ to have semisimple rank 1 in the study of reductive groups (these are the groups whose unipotent radical $R(G)_u$ is trivial). Precisely, we showed that such a $G$ must have a […]

## 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 […]