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A torsion theory in the category of cocommutative Hopf algebras

Abstract

The purpose of this article is to prove that the category of cocommutative Hopf KK-algebras, over a field KK 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 KK-algebras, respectively

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