Lie Theory for Hopf operads

Abstract : 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
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Pré-publication, Document de travail
23 pages. 2006
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https://hal.archives-ouvertes.fr/hal-00083757
Contributeur : Muriel Livernet <>
Soumis le : mardi 18 juillet 2006 - 15:31:30
Dernière modification le : mardi 11 octobre 2016 - 14:54:32
Document(s) archivé(s) le : lundi 5 avril 2010 - 23:45:55

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  • HAL Id : hal-00083757, version 1

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Muriel Livernet, Frédéric Patras. Lie Theory for Hopf operads. 23 pages. 2006. <hal-00083757>

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