%0 Journal Article
%T The infinitesimal Hopf algebra and the operads of planar forests
%A Lo£¿c Foissy
%J Mathematics
%D 2009
%I arXiv
%X 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.
%U http://arxiv.org/abs/0901.2202v1