Generators of a Sato-Tate group (reviewed)

The generators of a Sato-Tate group $G$ are a set $S$ of matrices $g$ that together with the identity component $G^0$ generate $G$.

The group $\langle S\rangle$ generated by $S$ necessarily contains representatives of every element of the component group but it will typically be larger (but not when $G^0$ is the trivial group, as in weight $0$).