On the Connes-Kreimer construction of Hopf Algebras

1999/07/14 by Ieke Moerdijk, I. Moerdijk, Moerdijk, I. · 3 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #math-ph #math.KT #math.MP #math.QA

paper · pdf · doi:10.48550/arxiv.math-ph/9907010

arxiv created 1999/07/14 · openalex publication_date 1999/07/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a universal construction of families of Hopf P-algebras for any Hopf operad P. As a special case, we recover the Connes-Kreimer Hopf algebra of rooted trees.

Citations

• Koszul duality for operads

Cited by

• Generalized Connes-Kreimer Hopf algebras on decorated rooted forests by weighted cocycles
• Cocycle weighted infinitesimal bialgebras and pre-Lie algebras on rooted trees
• Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach

Related

• Relating the Connes-Kreimer and Grossman-Larson Hopf algebras built on rooted trees
• Some Hopf Algebras of Trees
• Connes-Moscovici-Kreimer Hopf Algebras
• Generalized Connes-Kreimer Hopf algebras on decorated rooted forests by weighted cocycles
• Polynomial realizations of some combinatorial Hopf algebras