多项式不变量的胶合构造
A gluing construction for polynomial invariants
摘要：
本文给出了两个群$G_X\subseteq GL(\ell,\mathbb F)$和$G_Y\subseteq GL(m,\mathbb F)$的多项式胶合构造，得到了一个群$G\subseteq GL(\ell+m,\mathbb F)$，其不变量环同构于$G_X$和$G_Y$的不变量环的张量积.特别是，这一结果使我们能够获得许多组多项式环的不变量，包括所有的$p$ -组的不变量环是多项式的$\mathbb F_p$，和有限子群的$GL(n,\mathbb F)$定义的稀疏模式，推广了许多已知的例子。
英文摘要：
We give a polynomial gluing construction of two groups $G_X\subseteq GL(\ell,\mathbb F)$ and $G_Y\subseteq GL(m,\mathbb F)$ which results in a group $G\subseteq GL(\ell+m,\mathbb F)$ whose ring of invariants is isomorphic to the tensor product of the rings of invariants of $G_X$ and $G_Y$. In particular, this result allows us to obtain many groups with polynomial rings of invariants, including all $p$-groups whose rings of invariants are polynomial over $\mathbb F_p$, and the finite subgroups of $GL(n,\mathbb F)$ defined by sparsity patterns, which generalize many known examples.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
