1203.2686 (Alastair Hamilton)

A nondiagrammatic description of the Connes-Kreimer Hopf algebra    [PDF]

Alastair Hamilton

We demonstrate that the fundamental algebraic structure underlying the Connes-Kreimer Hopf algebra -- the insertion pre-Lie structure on graphs -- corresponds directly to the canonical pre-Lie structure of polynomial vector fields. Using this fact, we construct a Hopf algebra built from tensors that is isomorphic to a version of the Connes-Kreimer Hopf algebra that first appeared in the perturbative renormalization of quantum field theories.

View original: http://arxiv.org/abs/1203.2686