The infinitesimal Hopf algebra and the operads of planar forests

2009/01/15 by Foissy, Loïc · 1 citation
#05C05 #16W30 #18D50. #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.0901.2202

Abstract

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.

Cited by

• Cocycle weighted infinitesimal bialgebras and pre-Lie algebras on rooted trees

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