Some Hopf Algebras of Trees

Details Some Hopf Algebras of Trees Some Hopf Algebras of Trees

2001-06-28

arxiv.org/abs/math/0106244v3

Mathematics

Quantum Algebra

24 pages, 3 figures

Scientific paper

This paper generalizes the operadic construction of the Connes-Kreimer Hopf algebra of rooted trees by Moerdijk. Examples of Hopf algebras obtained in this way include the Loday-Ronco Hopf algebra of planar binary trees and the Brouder-Frabetti pruning Hopf algebra. In some examples we obtain a natural pre-Lie or dendriform algebra structure on the dual Hopf algebra. v2: Proof in section 8 corrected. v3: more corrections.

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