Notes for AKT-090929/0:09:24

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Theorem (Milnor-Moore): A graded, connected, co-commutative bialgebra is the universal enveloping algebra of its space of primitives:

[math]\displaystyle{ \mathcal{A}=U(\mathcal{P}(\mathcal{A})) }[/math]

(A proof is given here.)