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${\mathfrak{A}}$-GENERATORS FOR THE POLYNOMIAL ALGEBRA OF FIVE VARIABLES IN DEGREE 5(2t - 1) + 6 · 2t

  • Phuc, Dang Vo (Faculty of Education Studies University of Khanh Hoa)
  • Received : 2019.02.26
  • Accepted : 2019.05.16
  • Published : 2020.04.30
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Abstract

Let Ps := 𝔽2[x1, x2, …, xs] = ⊕n⩾0(Ps)n be the polynomial algebra viewed as a graded left module over the mod 2 Steenrod algebra, ${\mathfrak{A}}$. The grading is by the degree of the homogeneous terms (Ps)n of degree n in the variables x1, x2, …, xs of grading 1. We are interested in the hit problem, set up by F. P. Peterson, of finding a minimal system of generators for ${\mathfrak{A}}$-module Ps. Equivalently, we want to find a basis for the 𝔽2-graded vector space ${\mathbb{F}}_2{\otimes}_{\mathfrak{A}}$ Ps. In this paper, we study the hit problem in the case s = 5 and the degree n = 5(2t - 1) + 6 · 2t with t an arbitrary positive integer.

Keywords

Acknowledgement

I would like to give my deepest sincere thanks to Assoc. Prof. Nguyen Sum for many valuable discussions and his help in finding some strictly inadmissible monomials in this article.

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