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arXiv · 1502.05569

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
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Abstract

Denote by $P_k$ the graded polynomial algebra $\mathbb F_2[x_1,x_2,\ldots ,x_k]$ over the prime field of two elements, $\mathbb F_2$, with the degree of each $x_i$ being 1. We study the Peterson hit problem of determining 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 $P_k$ in the case $k=5$ and the degree $4(2^d - 1)$ with $d$ an arbitrary positive integer.

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Dang Vo Phuc, Nguyen Sum. 2015-02-19. On a minimal set of generators for the polynomial algebra of five variables as a module over the Steenrod algebra. https://doi.org/10.1007/s40306-016-0190-z

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