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

Authors
Panaite, F
Citation
F. Panaite, Relating the Connes-Kreimer and Grossman-Larson Hopf algebras built on rooted trees, LETT MATH P, 51(3), 2000, pp. 211-219
Citations number
10
Categorie Soggetti
Physics
Journal title
LETTERS IN MATHEMATICAL PHYSICS
ISSN journal
03779017 → ACNP
Volume
51
Issue
3
Year of publication
2000
Pages
211 - 219
Database
ISI
SICI code
0377-9017(200002)51:3<211:RTCAGH>2.0.ZU;2-V
Abstract
We prove that there is a Hopf duality between two Hopf algebras built on ro oted trees: the Connes-Kreimer Hopf algebra H-R which controls the renormal ization in quantum field theory, and the Grossman-Larson Hopf algebra A int roduced ten years ago through some 'differential' and combinatorial reason. We then study two natural operators on A, inspired by similar ones introdu ced by Connes and Kreimer for H-R.