Milnor–Moore theorem

In algebra, the Milnor–Moore theorem, introduced in (Milnor–Moore 1965), states: given a connected graded cocommutative Hopf algebra A over a field of characteristic zero with dim ⁡ A n < ∞ , the natural Hopf algebra homomorphism

from the universal enveloping algebra of the "graded" Lie algebra P ( A ) of primitive elements of A to A is an isomorphism. (The universal enveloping algebra of a graded Lie algebra L is the quotient of the tensor algebra of L by the two-sided ideal generated by elements xy-yx - (-1)^|x||y|[x, y].)

This work may also be compared with that by E. Halpern [1958] listed below.