# Modular covariants of cyclic groups of order p

Article

Elmer, J. 2022. Modular covariants of cyclic groups of order p.

*Journal of Algebra.*598, pp. 134-155. https://doi.org/10.1016/j.jalgebra.2022.01.015

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

Title | Modular covariants of cyclic groups of order p |

Authors | Elmer, J. |

Abstract | Let G be a cyclic group of order p and let V, W be kG-modules. We study the modules of covariants k[V,W]^G = (S(V^∗) ⊗ W)^G . Recall that G has exactly p inequivalent indecomposable kG-modules, denoted V_n (n = 1, . . . , p) and V_n has dimension n. For any n, we show that k[V_2,V_n]^G is a free k[V_2]^G- module (recovering a result of Broer and Chuai) and we give an explicit set of covariants generating k[V_2,V_n]^G freely over k[V_2]^G . For any n, we show that k[V_3,V_n]^G is a Cohen-Macaulay k[V_3]^G -module (again recovering a result of Broer and Chuai) and we give an explicit set of covariants which generate k[V 3 , V n ] G freely over a homogeneous system of parameters for k[V_3]^G . We also use our results to compute a minimal generating set for the transfer ideal of k[V_3]^G over a homogeneous system of parameters. |

Keywords | Modular invariant theory; Covariants; Free module; Cohen-Macaulay; Hilbert series |

Publisher | Elsevier |

Journal | Journal of Algebra |

ISSN | 0021-8693 |

Electronic | 1090-266X |

Publication dates | |

Online | 03 Feb 2022 |

Print | 15 May 2022 |

Publication process dates | |

Deposited | 03 Feb 2022 |

Submitted | 14 Nov 2019 |

Accepted | 29 Jan 2022 |

Output status | Published |

Publisher's version | License File Access Level Open |

Accepted author manuscript | License File Access Level Restricted |

Copyright Statement | © 2022 The Author. Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). |

Digital Object Identifier (DOI) | https://doi.org/10.1016/j.jalgebra.2022.01.015 |

Web of Science identifier | WOS:000793251800008 |

Language | English |

https://repository.mdx.ac.uk/item/89q79

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