On the Connes-Kreimer construction of Hopf Algebras

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.

References in corpus (3)

• Hopf Algebras, Renormalization and Noncommutative Geometry
• Operads, homotopy algebra and iterated integrals for double loop spaces
• Hopf algebras, cyclic cohomology and the transverse index theory

Cited by in corpus (14)

• Combinatorial Hopf algebras
• Compatible associative products and trees
• On Hopf algebra structures over operads
• Hopf algebra of multi-decorated rooted forests, free matching Rota-Baxter algebras and Gröbner-Shirshov bases
• Cacti and filtered distributive laws
• Polynomial functors and combinatorial Dyson-Schwinger equations
• Some Hopf Algebras of Trees
• Categorification of Hopf algebras of rooted trees
• QED Hopf algebras on planar binary trees
• Weighted infinitesimal bialgebras
• On Hopf algebra structures over free operads
• Locality and renormalisation: universal properties and integrals on trees
• The bigraft algebras
• A Hopf algebra on subgraphs of a graph