Frobenius representation type for invariant rings of finite groups
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866910644865859584 |
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| author | Hashimoto, Mitsuyasu Singh, Anurag K. |
| author_facet | Hashimoto, Mitsuyasu Singh, Anurag K. |
| contents | Let $V$ be a finite rank vector space over a perfect field of characteristic $p>0$, and let $G$ be a finite subgroup of $\operatorname{GL}(V)$. If $V$ is a permutation representation of $G$, or more generally a monomial representation, we prove that the ring of invariants $(\operatorname{Sym}V)^G$ has finite Frobenius representation type. We also construct an example with $V$ a finite rank vector space over the algebraic closure of the function field ${\mathbb{F}_3}(t)$, and $G$ an elementary abelian subgroup of $\operatorname{GL}(V)$, such that the invariant ring $(\operatorname{Sym}V)^G$ does not have finite Frobenius representation type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_11786 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Frobenius representation type for invariant rings of finite groups Hashimoto, Mitsuyasu Singh, Anurag K. Commutative Algebra Primary 13A50, Secondary 13A35 Let $V$ be a finite rank vector space over a perfect field of characteristic $p>0$, and let $G$ be a finite subgroup of $\operatorname{GL}(V)$. If $V$ is a permutation representation of $G$, or more generally a monomial representation, we prove that the ring of invariants $(\operatorname{Sym}V)^G$ has finite Frobenius representation type. We also construct an example with $V$ a finite rank vector space over the algebraic closure of the function field ${\mathbb{F}_3}(t)$, and $G$ an elementary abelian subgroup of $\operatorname{GL}(V)$, such that the invariant ring $(\operatorname{Sym}V)^G$ does not have finite Frobenius representation type. |
| title | Frobenius representation type for invariant rings of finite groups |
| topic | Commutative Algebra Primary 13A50, Secondary 13A35 |
| url | https://arxiv.org/abs/2312.11786 |