Lie theory for Hopf operads

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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.
23 pages. Using xyPic

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Rings and Algebras, Quantum Algebra, 18D50: 16W30: 17A30: 17B63

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http://salesiana.dossiersoluciones.com/handle/123456789/113879

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0606329
 http://arxiv.org/abs/math/0606329

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arXiv