On a minimal set of generators for the polynomial algebra of five variables as a module over the Steenrod algebra

Dang Vo Phuc, Nguyen Sum

Published 2015-02-19Version 1

Write $P_k:= \mathbb F_2[x_1,x_2,\ldots ,x_k]$ for the polynomial algebra over the prime field of two elements, $\mathbb F_2$, in $k$ variables $x_1, x_2, \ldots , x_k$, each of degree 1. We study the hit problem, set up by F. Peterson, of finding a minimal set of generators for $P_k$ as a module over the mod-2 Steenrod algebra, $\mathcal{A}$. In this paper, we explicitly determine a minimal set of $\mathcal A$-generators for $P_k$ with $k=5$ and in degree $2^{s+2} -4$ with $s$ an arbitrary positive integer.