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arXiv 2011.074082020-11-14math.RTmath.AC

Separating invariants over finite fields

Gregor Kemper, Artem Lopatin, Fabian Reimers

备注：: 18 pages
发表信息：: Journal of Pure and Applied Algebra, 226 (2022), 106904
DOI：: 10.1016/j.jpaa.2021.106904

英文摘要：

We determine the minimal number of separating invariants for the invariant ring of a matrix group $G < \mathrm{GL}_n(\mathbb{F}_q)$ over the finite field $\mathbb{F}_q$. We show that this minimal number can be obtained with invariants of degree at most $|G|n(q-1)$. In the non-modular case this construction can be improved to give invariants of degree at most $n(q-1)$. As examples we study separating invariants over the field $\mathbb{F}_2$ for two important representations of the symmetric group

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