# The relative Heller operator and relative cohomology for the Klein 4-group

Article

Elmer, J. 2022. The relative Heller operator and relative cohomology for the Klein 4-group.

*Communications in Algebra.*50 (4), pp. 1518-1534. https://doi.org/10.1080/00927872.2021.1984496

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

Title | The relative Heller operator and relative cohomology for the Klein 4-group |

Authors | Elmer, J. |

Abstract | Let G be the Klein Four-group and let k be an arbitrary field of characteristic 2. A classification of indecomposable kG-modules is known. We calculate the relative cohomology groups H^i_χ(G,N) for every indecomposable kG-module N , where χ is the set of proper subgroups in G. This extends work of Pamuk and Yalcin to cohomology with non-trivial coefficients. We also show that all cup products in strictly positive degree in H^*_χ (G, k) are trivial. |

Keywords | Cohomology of groups; cup product; modular representation theory; relative cohomology |

Language | English |

Publisher | Taylor and Francis |

Journal | Communications in Algebra |

ISSN | 0092-7872 |

Electronic | 1532-4125 |

Publication dates | |

Online | 16 Oct 2021 |

Print | 03 Apr 2022 |

Publication process dates | |

Submitted | 24 Jun 2021 |

Accepted | 20 Sep 2021 |

Deposited | 22 Sep 2021 |

Output status | Published |

Accepted author manuscript | |

Copyright Statement | This is an Accepted Manuscript of an article published by Taylor & Francis in Communications in Algebra on 16 Oct 2021, available online: http://www.tandfonline.com/10.1080/00927872.2021.1984496 |

Digital Object Identifier (DOI) | https://doi.org/10.1080/00927872.2021.1984496 |

Web of Science identifier | WOS:000707828500001 |

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