Milnor–Moore theorem
In algebra, the Milnor–Moore theorem, introduced by John W. Milnor and John C. Moore (1965) classifies an important class of Hopf algebras, of the sort that often show up as cohomology rings in algebraic topology. The theorem states: given a connected, graded, cocommutative Hopf algebra A over a field of characteristic zero with dim A n < ∞ {\displaystyle \dim A_{n}<\infty } for all n, the natural Hopf algebra homomorphism U ( P ( A ) ) → A {\displaystyle U(P(A))\to A} from the universal enveloping algebra of the graded Lie algebra P ( A ) {\displaystyle P(A)} of primitive elements of A to A is an isomorphism.