Relating the Connes-Kreimer and Grossman-Larson Hopf algebras built on rooted trees

Details Relating the Connes-Kreimer and Grossman-Larson Hopf algebras built on rooted trees Relating the Connes-Kreimer and Grossman-Larson Hopf algebras built on rooted trees

2000-03-13

arxiv.org/abs/math/0003074v1

Mathematics

Quantum Algebra

8 pages, Latex, no figures

Scientific paper

We find a relation between two Hopf algebras built on rooted trees. The first is the Connes-Kreimer Hopf algebra H_R which describes a certain type of renormalization in quantum field theory; the second is the Grossman-Larson Hopf algebra A introduced ten years ago by some "differential" and combinatorial reasons. Roughly, the relation is the following: there exists a duality between these two Hopf algebras. We study then two natural operators on A, inspired by similar ones introduced by Connes and Kreimer for H_R.

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