Gabriel Kadjo’s research while affiliated with Catholic University of Louvain and other places

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Publications (5)


Split extension classifiers in the category of cocommutative Hopf algebras
  • Article
  • Full-text available

September 2018

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86 Reads

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15 Citations

Bulletin of the Belgian Mathematical Society - Simon Stevin

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Gabriel Kadjo

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We describe the split extension classifiers in the semi-abelian category of cocommutative Hopf algebras over an algebraically closed field of characteristic zero. The categorical notions of centralizer and of center in the category of cocommutative Hopf algebras is then explored. We show that the categorical notion of center coincides with the one that is considered in the theory of general Hopf algebras.

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Split extension classifiers in the category of cocommutative Hopf algebras

We describe the split extension classifiers in the semi-abelian category of cocommutative Hopf algebras over an algebraically closed field of characteristic zero. The categorical notions of centralizer and of center in the category of cocommutative Hopf algebras is then explored. We show that the categorical notion of center coincides with the one that is considered in the theory of general Hopf algebras.



A Torsion Theory in the Category of Cocommutative Hopf Algebras

March 2015

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175 Reads

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36 Citations

Applied Categorical Structures

The purpose of this article is to prove that the category of cocommutative Hopf Kalgebras, over a field K of characteristic zero, is a semi-abelian category. Moreover, we show that this category 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


A torsion theory in the category of cocommutative Hopf algebras

February 2015

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24 Reads

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2 Citations

The purpose of this brief article is to prove that the category HopfK,coc\textbf{Hopf}_{K,coc} of cocommutative Hopf K-algebras, over a field K of characteristic zero, constitute a semi-abelian category. Then in the semi-abelian context, we shall show that HopfK,coc\textbf{Hopf}_{K,coc} has a torsion theory whose "torsion" and "torsion-free" parts are respectively given by group Hopf algebras and universal enveloping of Lie K-algebras.

Citations (3)


... A context for the general analysis. An appropriate context is the setting of semi-abelian categories in the sense of Janelidze-Márki-Tholen [19]: it includes the three types of algebraic structures as examples (see [14] for the Hopf algebra case), next to any type of (universal) algebras containing a group operation and a single constant in their signature (the varieties of Ω-groups of Higgins [18]), as well as some "strange" categories such as loops, Heyting semilattices and the dual of the category of pointed sets (see [4,9] for an overview). By definition, a category X is semi-abelian if and only if it is pointed, Barr exact, Bourn protomodular with binary coproducts. ...

Reference:

A universal Kaluzhnin--Krasner embedding theorem
Split extension classifiers in the category of cocommutative Hopf algebras

Bulletin of the Belgian Mathematical Society - Simon Stevin

... We observe that the forgetful functors F · , F • : HBR coc → Hopf k,coc send the short exact sequence (12) to the canonical short exact sequence in the hereditary torsion theory (PrimHopf k , GrpHopf k ) in Hopf k,coc [23,Theorem 4.3]. These are so torsion theory functors in the sense of [7]. ...

A Torsion Theory in the Category of Cocommutative Hopf Algebras

Applied Categorical Structures

... The original example of a torsion theory is, of course, that in the category of abelian groups, with the usual notions of torsion group and torsion-free group. Tens of papers have been devoted to torsion theories in various non-abelian contexts, including [9,11,30,24,21,18,10,29,12,22]. For a first easy example of a pretorsion theory, consider the category PreOrd of preordered sets. ...

A torsion theory in the category of cocommutative Hopf algebras
  • Citing Article
  • February 2015