On the antipode of Kreimer's Hopf algebra
Hector Figueroa, Jose M. Gracia-Bondia
Abstract
We give a new formula for the antipode of the algebra of rooted trees, directly in terms of the bialgebra structure. The equivalence, proved in this paper, among the three available formulae for the antipode, reflects the equivalence among the Bogoliubov-Parasiuk-Hepp, Zimmermann, and Dyson-Salam renormalization schemes.
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