Milnor–Moore theorem
In algebra, the Milnor–Moore theorem, introduced by , states: given a connected, graded, cocommutative Hopf algebra A over a field of characteristic zero with for all n, the natural Hopf algebra homomorphism
from the universal enveloping algebra of the graded Lie algebra of primitive elements of A to A is an isomorphism.
In algebraic topology, the term usually refers to the corollary of the aforementioned result, that for a pointed, simply connected space X, the following isomorphism holds:
where denotes the loop space of X,
compare with Theorem 21.5 from. This work may also be compared with that of.
