A gluing construction for polynomial invariants

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Abstract

We give a polynomial gluing construction of two groups GX⊆GL(ι,F) and GY⊆GL(m,F) which results in a group G⊆GL(ι+m,F) whose ring of invariants is isomorphic to the tensor product of the rings of invariants of GX and GY. 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 Fp, and the finite subgroups of GL(n,F) defined by sparsity patterns, which generalize many known examples.

Original languageEnglish (US)
Pages (from-to)432-442
Number of pages11
JournalJournal of Algebra
Volume328
Issue number1
DOIs
Publication statusPublished - Feb 15 2011

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Keywords

  • Polynomial gluing
  • Ring of invariants
  • Sparsity groups

ASJC Scopus subject areas

  • Algebra and Number Theory

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