Relating two Hopf algebras built from an operad

Details Relating two Hopf algebras built from an operad Relating two Hopf algebras built from an operad

2007-07-25

arxiv.org/abs/0707.3725v2

International Mathematics Research Notices 2007 (2007) rnm131, 27 pages

Mathematics

Rings and Algebras

21 pages, use graphics, 12 figures Version 2 : references added, minor changes. This version has not been corrected after subm

Scientific paper

10.1093/imrn/rnm131

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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