A minimal set of generators for the polynomial algebra of five variables in a generic degree

2023/12/28 by Nguyễn Sum, Sum, Nguyen, Phạm Ðỗ Tài +1 · 1 citation
Mathematics · Physics and Astronomy · #55S10 #Advanced Differential Equations and Dynamical Systems #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #Primary 55S05

paper · pdf · doi:10.48550/arxiv.2312.16803

openalex publication_date 2023/12/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let P_k be the graded polynomial algebra \mathbb F₂[x₁,x₂,… ,x_k] over the prime field with two elements, \mathbb F₂, with the degree of each x_i being 1. We study the hit problem, set up by Frank Peterson, of finding a minimal set of generators for P_k as a module over the mod-2 Steenrod algebra, A. It is an open problem in Algebraic Topology. In this paper, we explicitly determine a minimal set of A-generators for P₅ in the case of the generic degree m = 2^d for all d \geqslant 8.

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• A matrix criterion and algorithmic approach for the Peterson hit problem: Part I

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