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On the duality of generalized Lie and Hopf algebras

par Vercruysse, Joost ;Goyvaerts, Isar
Référence Advances in mathematics, 258, page (154-190)
Publication Publié, 2014

Article révisé par les pairs

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Résumé :

We show how, under certain conditions, an adjoint pair of braided monoidal functors can be lifted to an adjoint pair between categories of Hopf algebras. This leads us to an abstract version of Michaelis' theorem, stating that given a Hopf algebra H, there is a natural isomorphism of Lie algebras Q(H) * ≅ P(H {ring operator}), where Q(H) * is the dual Lie algebra of the Lie coalgebra of indecomposables of H, and P(H {ring operator}) is the Lie algebra of primitive elements of the Sweedler dual of H. We apply our theory to Turaev's Hopf group-(co)algebras. © 2014 Elsevier Inc.