Lie theory for Hopf operads

Details Lie theory for Hopf operads Lie theory for Hopf operads

2006-06-14

arxiv.org/abs/math/0606329v1

Mathematics

Rings and Algebras

23 pages. Using xyPic

Scientific paper

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.

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