Modular invariants of a vector and a covector for some elementary abelian $p$-groups
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866910453300461568 |
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| author | Ren, Shan |
| author_facet | Ren, Shan |
| contents | Let $\mathbb{F}_p$ be the prime field of order $p>0$ and $G$ be an elementary abelian $p$-group.For some $n$-dimensional cohyperplane $G$-representations $V$ over $\mathbb{F}_p$, we show that $\mathbb{F}_p[V\oplus V^*]^G$, the invariant ring of a vector and a covector is a complete intersection by exhibiting an explicit generating set (in fact, a SAGBI basis) and exposing all relations among the generators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_07520 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Modular invariants of a vector and a covector for some elementary abelian $p$-groups Ren, Shan Commutative Algebra 13A50 Let $\mathbb{F}_p$ be the prime field of order $p>0$ and $G$ be an elementary abelian $p$-group.For some $n$-dimensional cohyperplane $G$-representations $V$ over $\mathbb{F}_p$, we show that $\mathbb{F}_p[V\oplus V^*]^G$, the invariant ring of a vector and a covector is a complete intersection by exhibiting an explicit generating set (in fact, a SAGBI basis) and exposing all relations among the generators. |
| title | Modular invariants of a vector and a covector for some elementary abelian $p$-groups |
| topic | Commutative Algebra 13A50 |
| url | https://arxiv.org/abs/2305.07520 |