The admissible monomial bases for the polynomial algebra of five variables in some types of generic degrees
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866914924537577472 |
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| author | Sum, Nguyen |
| author_facet | Sum, Nguyen |
| contents | Let $P_k$ be 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 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, $\mathcal{A}.$ In this paper, we explicitly determine a minimal set of $\mathcal{A}$-generators for $P_5$ in the case of the degrees $n = 2^{d+1} - 1$ and $n = 2^{d+1} - 2$ for all $d \geqslant 6$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_12543 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The admissible monomial bases for the polynomial algebra of five variables in some types of generic degrees Sum, Nguyen Algebraic Topology 55S10, Secondary: 55S05 Let $P_k$ be 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 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, $\mathcal{A}.$ In this paper, we explicitly determine a minimal set of $\mathcal{A}$-generators for $P_5$ in the case of the degrees $n = 2^{d+1} - 1$ and $n = 2^{d+1} - 2$ for all $d \geqslant 6$. |
| title | The admissible monomial bases for the polynomial algebra of five variables in some types of generic degrees |
| topic | Algebraic Topology 55S10, Secondary: 55S05 |
| url | https://arxiv.org/abs/2209.12543 |