The infinitesimal Hopf algebra and the operads of planar forests

Details The infinitesimal Hopf algebra and the operads of planar forests The infinitesimal Hopf algebra and the operads of planar forests

2009-01-15

arxiv.org/abs/0901.2202v1

Mathematics

Rings and Algebras

30 pages

Scientific paper

We introduce two operads which own the set of planar forests as a basis. With its usual product and two other products defined by different types of graftings, the algebra of planar rooted trees H becomes an algebra over these operads. The compatibility with the infinitesimal coproduct of H and these structures is studied. As an application, an inductive way of computing the dual basis of H for its infinitesimal pairing is given. Moreover, three Cartier-Quillen-Milnor-Moore theorems are given for the operads of planar forests and a rigidity theorem for one of them.

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