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arXiv · 0707.3725

Relating two Hopf algebras built from an operad

Frédéric Chapoton·Muriel Livernet
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Abstract

Starting from an operad, one can build a family of posets. From this family of posets, one can define an incidence Hopf algebra. By another construction, one can also build a group directly from the operad. We then consider its Hopf algebra of functions. We prove that there exists a surjective morphism from the latter Hopf algebra to the former one. This is illustrated by the case of an operad built on rooted trees, the $\NAP$ operad, where the incidence Hopf algebra is identified with the Connes-Kreimer Hopf algebra of rooted trees.

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Frédéric Chapoton, Muriel Livernet. 2007-10-25. Relating two Hopf algebras built from an operad. https://doi.org/10.1093/imrn%2Frnm131

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