= Period obstruction to integration of a Lie algebra homomorphism
{title2=$\widetilde\Phi(\ker p)=\{e\}$}
For a connected source, first integrate on its <universal covering Lie group>. The resulting map descends to the original <group> exactly when it kills the discrete kernel of the <covering map>. For the <circle group>, a real-linear map $t\mapsto ct$ integrates to a circle <endomorphism> exactly when $c\in\mathbb Z$, since $2\pi\mathbb Z$ must map into itself. This is a global period condition invisible to the zero bracket of the circle's <Lie algebra>.
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