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

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.

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.

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

The purpose of this brief article is to prove that the category $\textbf{Hopf}_{K,coc}$ 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 $\textbf{Hopf}_{K,coc}$ has a torsion theory whose "torsion" and "torsion-free" parts are respectively given by group Hopf algebras and universal enveloping of Lie K-algebras.