摘要
We introduce two operads based on the set of planar forests. 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.
- 出版日期2010