### 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 language | English (US) |
---|---|

Pages (from-to) | 432-442 |

Number of pages | 11 |

Journal | Journal of Algebra |

Volume | 328 |

Issue number | 1 |

DOIs | |

State | Published - Feb 15 2011 |

### Fingerprint

### Keywords

- Polynomial gluing
- Ring of invariants
- Sparsity groups

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Journal of Algebra*,

*328*(1), 432-442. https://doi.org/10.1016/j.jalgebra.2010.09.010

**A gluing construction for polynomial invariants.** / Huang, Jia.

Research output: Contribution to journal › Article

*Journal of Algebra*, vol. 328, no. 1, pp. 432-442. https://doi.org/10.1016/j.jalgebra.2010.09.010

}

TY - JOUR

T1 - A gluing construction for polynomial invariants

AU - Huang, Jia

PY - 2011/2/15

Y1 - 2011/2/15

N2 - 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.

AB - 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.

KW - Polynomial gluing

KW - Ring of invariants

KW - Sparsity groups

UR - http://www.scopus.com/inward/record.url?scp=78650035860&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78650035860&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2010.09.010

DO - 10.1016/j.jalgebra.2010.09.010

M3 - Article

AN - SCOPUS:78650035860

VL - 328

SP - 432

EP - 442

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

IS - 1

ER -