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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