# On the depth of modular invariant rings for the groups C_p x C_p

Book chapter

Elmer, J. and Fleischmann, P. 2009. On the depth of modular invariant rings for the groups C_p x C_p. in: Symmetry and Spaces: in honour of Gerry Schwarz Birkhauser Boston.

Chapter title | On the depth of modular invariant rings for the groups C_p x C_p |
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Authors | Elmer, J. and Fleischmann, P. |

Abstract | Let G be a finite group, k a field of characteristic p and V a finite dimensional kG-module. Let R denote the symmetric algebra over the dual space V∗ with G acting by graded algebra automorphisms. Then it is known that the depth of the invariant ring R^G is at least min {dim(V), dim(V^P)+cc_G(R)+1}. A module V for which the depth of R^G 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 C_p × C_p, generating many new examples of flat modules. We introduce the useful notion of “strongly flat” modules, classi-fying them for the group C_2 × C_2, as well as determining the depth of R^G for any indecomposable modular representation of C_2 × C_2. |

Book title | Symmetry and Spaces: in honour of Gerry Schwarz |

Publisher | Birkhauser Boston |

Series | Progress in Mathematics |

ISBN | |

Hardcover | 9780817648749 |

Publication dates | |

Print | 14 Nov 2009 |

Publication process dates | |

Deposited | 14 Apr 2016 |

Output status | Published |

Copyright Statement | Access to full text restricted pending copyright check |

Digital Object Identifier (DOI) | https://doi.org/10.1007/978-0-8176-4875-6_4 |

Language | English |

https://repository.mdx.ac.uk/item/863v3

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