Abstract
We relate the algebra of planar rooted trees introduced in the first part [6] to several algebras of trees: the Brouder-Frabetti algebra of binary trees, the deformations of Moerdijk and van der Laan, the free dendriform algebra of Loday and Ronco, and the Grossman–Larson algebra. We construct a subalgebra of H D P,R which plays the role played by the Connes–Moscovici algebra in the case of the Connes–Kreimer algebra.
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