On the duality of generalized Lie and Hopf algebras

Isar Goyvaerts, Joost Vercruysse

Research output: Contribution to journalArticle

4 Citations (Scopus)


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 $Q(H)^*\cong P(H^\circ)$, where $Q(H)^*$ is the dual Lie algebra of the Lie coalgebra of indecomposables of $H$, and $P(H^\circ)$ is the Lie algebra of primitive elements of the Sweedler dual of $H$. We apply our theory to Turaev's Hopf group-(co)algebras.
Original languageEnglish
Pages (from-to)154-190
JournalAdvances in Mathematics
Publication statusPublished - 2014


  • Lie algebra
  • Lie coalgebra
  • Hopf algebra
  • duality


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