Abstract:
In a recent paper Buchstaber and the author introduced a new structure in the cohomology of Hopf algebras, in terms of the Buchstaber spectral sequence ($\mathrm{Bss}$). The classical Steenrod algebra $\mathcal{A}_2$ contains the important Hopf subalgebra $A(1)$, whose cohomology is long known. We fully calculate the structure under consideration on this cohomology. In the framework of the demonstration of the methods of $\mathrm{Bss}$ we solve an inverse problem: we present a new explicit computation of the $s$th cohomology of $A(1)$ for $s\le 4$. We also use methods of $\mathrm{Bss}$ to obtain some results on Massey products and relations in the cohomology of the Steenrod algebras $\mathcal{A}_p$ for $p\ge 2$.
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