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arXiv · 1203.2686

A nondiagrammatic description of the Connes-Kreimer Hopf algebra

Alastair Hamilton
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Abstract

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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Alastair Hamilton. 2012-03-13. A nondiagrammatic description of the Connes-Kreimer Hopf algebra. https://arxiv.org/abs/1203.2686

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