## Abstract

Let G be a finite group, k a field of characteristic p and V a finite dimensional
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 f “strongly flat” modules, classifying
them for the group C2 ×C2, as well as determining the depth of RG for any indecomposable modular representation of C2×C2.

Translated title of the contribution | On the Depth of Modular Invariant Rings for the GroupsCp×Cp |
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Original language | English |

Title of host publication | Symmetry and Spaces |

Editors | Campbell , H.E.A.E.; Helminck, A.G.; Kraft, D.L H.; Wehlau |

Publisher | Springer |

Pages | 45 - 63 |

Number of pages | 13 |

ISBN (Print) | 9780817648749 |

Publication status | Published - 2010 |