The Steenrod algebra and the automorphism group of additive formal group law (Q2574030)

The aim of this paper is to reprove a result of Milnor relating co-operations in mod \(2\) cohomology to automorphisms of the additive formal group law. Concretely, let \(H_*H\) be the Hopf algebra of stable co-operations in mod \(2\) ordinary cohomology, and let \(A_*\) be the Hopf algebra representing the functor which takes a non-negatively graded commutative \({\mathbb F}_2\)-algebra \(R_*\) to the set of strict automorphisms of the additive formal group law over \(R_*\). Milnor established that both of these objects, \(H_*H\) and \(A_*\), are isomorphic to the polynomial ring \({\mathbb F}_2[\xi_1, \xi_2, \dots]\) with coproduct \(\psi(\xi_n) = \sum_{i=0}^n \xi_{n-i}^{2^i} \otimes \xi_i\). He did this using the dual object, \(S_*\), which is generated by the Steenrod operations \(Sq^k\) (\(k > 0\)) subject to the Adem relations and satisfying the Cartan formula. The paper under review provides a direct proof, avoiding the use of \(S_*\).