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

Abstract

The mod 2 Steenrod algebra A(2) can be defined as the quotient of the mod 2 Leibniz-Hopf algebra F-2 by the Adem relations. Dually, the mod 2 dual Steenrod algebra A(2)(*)can be thought of as a sub-Hopf algebra of the mod 2 dual Leibniz-Hopf algebra F-2(*). We study A(2)(*)and F(2)(*)from this viewpoint and give generalisations of some classical results in the literature.