A nondiagrammatic description of the Connes-Kreimer Hopf algebra

Alastair Hamilton

doi:10.1016/j.jpaa.2012.06.027

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.

Original language	English
Pages (from-to)	449-469
Number of pages	21
Journal	Journal of Pure and Applied Algebra
Volume	217
Issue number	3
DOIs	https://doi.org/10.1016/j.jpaa.2012.06.027
State	Published - Mar 2013

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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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A nondiagrammatic description of the Connes-Kreimer Hopf algebra

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