A gluing construction for polynomial invariants

Details A gluing construction for polynomial invariants A gluing construction for polynomial invariants

2010-05-17

arxiv.org/abs/1005.2973v2

J. Algebra 328 (2011), 432-442

Mathematics

Commutative Algebra

10 pages, to appear in Journal of algebra

Scientific paper

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.

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