All Questions

$\DeclareMathOperator\Lie{Lie}$Let $G/K$ be a reductive group over a field $K$. In characteristic $0$ the Lie algebra is invariant under base change of fields, so to understand $\Lie(G)$ it is enough ...

Let $k$ be an algebraically closed field, $G$ a (smooth, connected) reductive algebraic group over $k$, $H$ a (smooth, connected) reductive group of semisimple rank 1, and $T$ a maximal torus in $H$. ...