The differential invariants of $SL_2(\mathbb{F}_3)$ acting on trace-free matrices over $\mathbb{F}_3$
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917142640721920 |
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| author | Elmer, Jonathan Meyer, Anja |
| author_facet | Elmer, Jonathan Meyer, Anja |
| contents | Let $M$ denote the vector space of $2 \times 2$ matrices with coefficients in $\mathbb{F}_3$ and trace zero. Let $G = SL_2(\mathbb{F}_3)$. Then $G$ acts on $M$ via conjugation. Let $R =(S(M^*) \otimes Λ(M^*))$ be the algebra of differential forms on $M$. We compute a minimal generating set for $R^G$ as a commutative-graded algebra. In doing so we utilise the theory of Cohen-Macaulay modules and results in the theory of covariants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_11702 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The differential invariants of $SL_2(\mathbb{F}_3)$ acting on trace-free matrices over $\mathbb{F}_3$ Elmer, Jonathan Meyer, Anja Commutative Algebra Let $M$ denote the vector space of $2 \times 2$ matrices with coefficients in $\mathbb{F}_3$ and trace zero. Let $G = SL_2(\mathbb{F}_3)$. Then $G$ acts on $M$ via conjugation. Let $R =(S(M^*) \otimes Λ(M^*))$ be the algebra of differential forms on $M$. We compute a minimal generating set for $R^G$ as a commutative-graded algebra. In doing so we utilise the theory of Cohen-Macaulay modules and results in the theory of covariants. |
| title | The differential invariants of $SL_2(\mathbb{F}_3)$ acting on trace-free matrices over $\mathbb{F}_3$ |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2512.11702 |