The mod 2 dual Steenrod algebra as a subalgebra of the mod 2 dual Leibniz-Hopf algebra

Abstract

The mod 2 Steenrod algebra ${\mathcal{A}}_2$ can be defined as the quotient of the mod 2 Leibniz--Hopf algebra ${\mathcal{F}}_2$ by the Adem relations. Dually, the mod 2 dual Steenrod algebra ${\mathcal{A}}_2^{\ast }$ can be thought of as a sub-Hopf algebra of the mod 2 dual Leibniz--Hopf algebra ${\mathcal{F}}_2^{\ast }$. We study ${\mathcal{A}}_2^{\ast }$ and ${\mathcal{F}}_2^{\ast }$ from this viewpoint and give generalisations of some classical results in the literature.