A nondiagrammatic description of the Connes-Kreimer Hopf algebra

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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 languageEnglish
Pages (from-to)449-469
Number of pages21
JournalJournal of Pure and Applied Algebra
Volume217
Issue number3
DOIs
StatePublished - Mar 2013

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