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A Torsion Theory in the Category of Cocommutative Hopf Algebras

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Abstract

The purpose of this article is to prove that the category of cocommutative Hopf K-algebras, over a field K of characteristic zero, is a semi-abelian category. Moreover, we show that this category is action representable, and that it contains a torsion theory whose torsion-free and torsion parts are given by the category of groups and by the category of Lie K-algebras, respectively.

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Authors and Affiliations

  1. Institut de Recherche en Mathématique et Physique, Université catholique de Louvain, Chemin du Cyclotron 2, 1348, Louvain-la-Neuve, Belgium

    Marino Gran & Gabriel Kadjo

  2. Département de Mathématique, Université Libre de Bruxelles, Boulevard du Triomphe, 1050, Bruxelles, Belgium

    Joost Vercruysse

Authors
  1. Marino Gran
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  2. Gabriel Kadjo
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  3. Joost Vercruysse
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Correspondence to Marino Gran.

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Gran, M., Kadjo, G. & Vercruysse, J. A Torsion Theory in the Category of Cocommutative Hopf Algebras. Appl Categor Struct 24, 269–282 (2016). https://doi.org/10.1007/s10485-015-9396-9

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  • DOI: https://doi.org/10.1007/s10485-015-9396-9

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