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Relating two Hopf algebras built from an operad. (English) Zbl 1144.18006
The aim of the paper is to relate two Hopf algebras built from an operad. The first one is the incidence Hopf algebra obtained from an operad via a family of posets. The second one is the Hopf algebra of functions of a group built from the operad. The author proves that there exists a surjective morphism from the second to the first Hopf algebra. This is illustrated for the NAP operad built on rooted trees.

MSC:
18D50 Operads (MSC2010)
16T05 Hopf algebras and their applications
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