32 citations · 64 across the 6 of their papers we have counts for
6 papers
Families of Hopf algebras of trees and pre-Lie algebras
Pepijn van der Laan, Ieke Moerdijk
Using methods from math-ph/9907010, we study families of Hopf algebra structures on coloured trees.
Coloured Koszul duality and strongly homotopy operads
Pepijn van der Laan
This paper proves Koszul duality for coloured operads and uses it to introduce strongly homotopy operads as a suitable homotopy invariant version of operads. It shows that rational…
Operads and the Hopf algebras of renormalisation
Pepijn van der Laan
Functors from (co)operads to bialgebras relate Hopf algebras that occur in renormalisation to operads, which simplifies the proof of the Hopf algebra axioms, and induces a characte…
The renormalisation bialgebra and operads
Pepijn van der Laan, Ieke Moerdijk
In a recent preprint, Brouder and Schmitt give a careful construction of a `renormalisation' Hopf algebra out of an arbitrary bialgebra. In this note, we point out that this is a s…
Operads up to Homotopy and Deformations of Operad Maps
Pepijn P. I. van der Laan
From the `cofree' cooperad on a collection together with a differential, we construct an -algebra structure on the total space that desc…
Some Hopf Algebras of Trees
Pepijn van der Laan
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-Ro…