Lie Theory for Hopf operads

Muriel Livernet (1) , Frédéric Patras (2)

1 LAGA - Laboratoire Analyse, Géométrie et Applications
2 JAD - Laboratoire Jean Alexandre Dieudonné

The present article takes advantage of the properties of algebras in the category of S-modules (twisted algebras) to investigate further the fine algebraic structure of Hopf operads. We prove that any Hopf operad P carries naturally the structure of twisted Hopf P-algebra. Many properties of classical Hopf algebraic structures are then shown to be encapsulated in the twisted Hopf algebraic structure of the corresponding Hopf operad. In particular, various classical theorems of Lie theory relating Lie polynomials to words (i.e. elements of the tensor algebra) are lifted to arbitrary Hopf operads. Full-text: PostScript, PDF, or

Mots clés: Operads; Hopf algebras

Domaines: Anneaux et algèbres [math.RA]

Muriel Livernet, Frédéric Patras. Lie Theory for Hopf operads. 2006. ⟨hal-00083757⟩