Elmer, Jonathan and Fleischmann, Peter
(2010)
*On the Depth of Modular Invariant Rings for the Groups Cp x Cp.*
In: Campbell, Eddy and Helminck, Aloysius G. and Hanspeter, Kraft and Wehlau, David L., eds.
Symmetry and Spaces: In Honor of Gerry Schwarz.
Progress in Mathematics , 278
.
Birkhäuser, Boston, pp. 45-61.
ISBN 9780817648749.
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Official URL http://dx.doi.org/10.1007/978-0-8176-4875-6 |

## Abstract

Let G be a finite group, k a field of characteristic p and V a finite dimen- sional kG-module. Let R :=Sym(V�), the symmetric algebra over the dual spaceV�, with G acting by graded algebra automorphisms. Then it is known that the depth of the invariant ring RG is at least min{dim(V),dim(VP)+ccG(R)+1}. A module V for which the depth of RG attains this lower bound was called flat by Fleischmann, Kemper and Shank [13]. In this paper some of the ideas in [13] are further developed and applied to certain representations of Cp ×Cp, generating many new examples of flat modules. We introduce the useful notion of “strongly flat” modules, classi- fying them for the group C2 ×C2, as well as determining the depth of RG for any indecomposable modular representation of C2×C2.

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

Divisions: | Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science |

Depositing User: | Peter Fleischmann |

Date Deposited: | 11 Oct 2012 11:25 |

Last Modified: | 09 Jul 2014 09:42 |

Resource URI: | https://kar.kent.ac.uk/id/eprint/31524 (The current URI for this page, for reference purposes) |

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