2 Combinatorial Hopf algebras

A., Hopf algebra structure of a model quantum field theory, Proceedings of the 26th International Colloquium on Group Theoretical Methods in Physics, New York 2006, Editor: S.

In this section we give the definitions of operads and algebras over an operad and we refer to Fresse [11] for more general theory on operads. We further state the main results of

Examples of such Hopf algebras are the Connes-Kreimer Hopf algebra of Feynman graphs, underlying the combinatorics of perturbative renormalization in quantum field theory [CK00].. or

A further non-commutative Hopf algebra of TAGs can be defined when considering only graphs of a given quantum field theoretical model and defin- ing the coproduct as the appropriate

We also obtain several other Hopf algebras, which, respectively, involve forests of planar rooted trees, some kind of graphs consisting of nodes with one parent and several children

In [BBGa] a simple description of modified traces was found in the case that C = H-mod is the category of finite-dimensional representations of a finite-dimensional pivotal

If the characteristic of the base field is zero, we prove that the Lie algebra of the primitive elements of such an object is free, and we deduce a characterization of the formal

The main point of the construction is a Hopf algebra morphism Θ from H o to the Hopf algebra of free quasi-symmetric functions FQSym [4, 17], also known as the Malvenuto-Reutenauer