# Depth and detection in modular invariant theory

Article

Elmer, J. 2009. Depth and detection in modular invariant theory.

*Journal of Algebra.*322 (5), pp. 1653-1666. https://doi.org/10.1016/j.jalgebra.2009.04.036

Type | Article |
---|---|

Title | Depth and detection in modular invariant theory |

Authors | Elmer, J. |

Abstract | Let G be a finite group acting linearly on a vector space V over a field of characteristic p dividing the group order, and let R denote S(V∗). We study the R^G modules H^i(G, R), for i ≥ 0 with R^G itself as a special case. There are lower bounds for depth of (H^i(G, R)) and for depth(R^G). We show that a certain sufficient condition for their attainment (due to Fleischmann, Kemper and Shank) may be modified to give a condition which is both necessary and sufficient. We apply our main result to classify the representations of the Klein four-group for which depth(R^G) attains its lower bound. We also use our new condition to show that the if G = P × Q, with P a p-group and Q an abelian p'-group, then the depth of R G attains its lower bound if and only if the depth of R^P does so. |

Language | English |

Publisher | Elsevier |

Journal | Journal of Algebra |

ISSN | 0021-8693 |

Publication dates | |

Print | 01 Sep 2009 |

Publication process dates | |

Deposited | 14 Apr 2016 |

Accepted | 24 Apr 2009 |

Output status | Published |

Additional information | Available online 12 May 2009 |

Digital Object Identifier (DOI) | https://doi.org/10.1016/j.jalgebra.2009.04.036 |

First submitted version |

https://repository.mdx.ac.uk/item/863v6

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