Some Hopf Algebras of Trees
Quantum Algebra
2007-05-23 v3 Mathematical Physics
math.MP
Abstract
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.
Keywords
Cite
@article{arxiv.math/0106244,
title = {Some Hopf Algebras of Trees},
author = {Pepijn van der Laan},
journal= {arXiv preprint arXiv:math/0106244},
year = {2007}
}
Comments
24 pages, 3 figures