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
TypeArticle
TitleThe relative Heller operator and relative cohomology for the Klein 4-group
AuthorsElmer, 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.

KeywordsCohomology of groups; cup product; modular representation theory; relative cohomology
PublisherTaylor and Francis
JournalCommunications in Algebra
ISSN0092-7872
Electronic1532-4125
Publication dates
Online16 Oct 2021
Print03 Apr 2022
Publication process dates
Submitted24 Jun 2021
Accepted20 Sep 2021
Deposited22 Sep 2021
Output statusPublished
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 identifierWOS:000707828500001
LanguageEnglish
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