Thursday, March 15, 2012

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.
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