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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2312.16803 |
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| _version_ | 1866918024569683968 |
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| author | Sum, Nguyen Tai, Pham Do |
| author_facet | Sum, Nguyen Tai, Pham Do |
| contents | Let $P_k$ be the graded polynomial algebra $\mathbb F_2[x_1,x_2,\ldots ,x_k]$ over the prime field with 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, $\mathcal{A}.$ It is an open problem in Algebraic Topology. In this paper, we explicitly determine a minimal set of $\mathcal{A}$-generators for $P_5$ in the case of the generic degree $m = 2^{d}$ for all $d \geqslant 8$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_16803 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A minimal set of generators for the polynomial algebra of five variables in a generic degree Sum, Nguyen Tai, Pham Do Algebraic Topology 55S10, Primary 55S05 Let $P_k$ be the graded polynomial algebra $\mathbb F_2[x_1,x_2,\ldots ,x_k]$ over the prime field with 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, $\mathcal{A}.$ It is an open problem in Algebraic Topology. In this paper, we explicitly determine a minimal set of $\mathcal{A}$-generators for $P_5$ in the case of the generic degree $m = 2^{d}$ for all $d \geqslant 8$. |
| title | A minimal set of generators for the polynomial algebra of five variables in a generic degree |
| topic | Algebraic Topology 55S10, Primary 55S05 |
| url | https://arxiv.org/abs/2312.16803 |