# Tag Archives: torus

## 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 5: Semisimple Automorphisms

Lately I've been reading a bit of Robert Steinberg's book, "Endomorphisms of Algebraic Groups", so I've decided to explain what I am reading for this series on linear algebraic groups, which will take us away from Lie algebras for a bit of time. Let $G$ be a linear algebraic group over an algebraically closed […]