An embedding for the $Esb 2$-term of the Adams spectral sequence

The mod2 Steenrod Algebra A is a quotient of the universal Steenrod algebra Q, the homogeneous quadratic algebra of cohomology operations in the category of H_∞-ring spectra. The authors consider a quadratic linear algebra Q_1 obtained by suitably changing the generators of Q in order to make the quotient map π : Q → A a map of augmented algebras. It turns out that the map induced in cohomology is a monomorphism. We also computes the Ext-group of Q_1 under a hypothesis of koszulness on Q.