Simply Connected Semisimple Algebraic Group

A semisimple algebraic group is a connected reductive group with trivial connected center (equivalently, its root datum has no torus factor).

A central isogeny $f:G_1\to G_2$ is a surjective morphism of connected algebraic groups with finite kernel contained in the center of $G_1$.

A semisimple group $G$ is simply connected if every central isogeny $H\to G$ is an isomorphism (equivalently, the cocharacter lattice $X_*(T)$ equals the coroot lattice for a maximal torus $T$).

In the letter: $G_e$ is chosen with “simply connected non-abelian factors” so that lattices and duals behave cleanly.