Fleischmann, Peter and Kemper, Gregor and Shank, R. James
(2005)
*
Depth and cohomological connectivity in modular invariant theory.
*
Transactions of the American Mathematical Society,
357
(9).
pp. 3605-3621.
ISSN 0002-9947.
(doi:https://doi.org/10.1090/S0002-9947-04-03591-3)
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Official URL http://dx.doi.org/10.1090/S0002-9947-04-03591-3 |

## Abstract

Let G be a finite group acting linearly on a finite-dimensional vector space V over a field K of characteristic p. Assume that p divides the order of G so that V is a modular representation and let P be a Sylow p-subgroup for G. De. ne the cohomological connectivity of the symmetric algebra S( V *) to be the smallest positive integer m such that H-m( G, S( V *)) not equal 0. We show that min {dim(K)(V-P) + m+ 1, dim(K)( V)} is a lower bound for the depth of S( V *) G. We characterize those representations for which the lower bound is sharp and give several examples of representations satisfying the criterion. In particular, we show that if G is p-nilpotent and P is cyclic, then, for any modular representation, the depth of S( V *) G is min {dim(K)(V-P) + 2, dim(K)(V)}.

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

Uncontrolled keywords: | Rings |

Subjects: | Q Science > QA Mathematics (inc Computing science) |

Divisions: | Faculties > Sciences > School of Mathematics Statistics and Actuarial Science |

Depositing User: | Judith Broom |

Date Deposited: | 19 Dec 2007 18:18 UTC |

Last Modified: | 19 May 2014 13:27 UTC |

Resource URI: | https://kar.kent.ac.uk/id/eprint/520 (The current URI for this page, for reference purposes) |

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