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 […]