Fleischmann, Peter,
Woodcock, Chris F.
(2013)
*
Galois ring extensions and localized modular rings of invariants of p-groups.
*
Transformation Groups,
18
(1).
pp. 131-147.
ISSN 1083-4362.
(doi:10.1007/s00031-012-9205-6)
(The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)
(KAR id:33275)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. | |

Official URL http://dx.doi.org/10.1007/s00031-012-9205-6 |

## Abstract

We apply recent results on Galois-ring extensions and trace surjective algebras to analyze dehomogenized modular invariant rings of finite p-groups, as well as related localizations. We describe criteria for the dehomogenized invariant ring to be polynomial or at least regular and we show that for regular affine algebras with possibly non-linear action by a p-group, the singular locus of the invariant ring is contained in the variety of the transfer ideal. If V is the regular module of an arbitrary finite p-group, or V is any faithful representation of a cyclic p-group, we show that there is a suitable invariant linear form, inverting which renders the ring of invariants into a "localized polynomial ring" with dehomogenization being a polynomial ring. This is in surprising contrast to the fact that for a faithful representation of a cyclic group of order larger than p, the ring of invariants itself cannot be a polynomial ring by a result of Serre. Our results here generalize observations made by Richman [R] and by Campbell and Chuai [CCH].

Item Type: | Article |
---|---|

DOI/Identification number: | 10.1007/s00031-012-9205-6 |

Subjects: |
Q Science > QA Mathematics (inc Computing science) > QA150 Algebra Q Science > QA Mathematics (inc Computing science) > QA171 Representation theory |

Divisions: | Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science |

Depositing User: | Christopher Woodcock |

Date Deposited: | 27 Feb 2013 00:07 UTC |

Last Modified: | 16 Nov 2021 10:10 UTC |

Resource URI: | https://kar.kent.ac.uk/id/eprint/33275 (The current URI for this page, for reference purposes) |

Woodcock, Chris F.: | https://orcid.org/0000-0003-4713-0040 |

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