Rooted trees and symmetric functions: Zhao's homomorphism and the commutative hexagon
Quantum Algebra
2009-11-09 v1 Combinatorics
Abstract
Recent work on perturbative quantum field theory has led to much study of the Connes-Kreimer Hopf algebra. Its (graded) dual, the Grossman-Larson Hopf algebra of rooted trees, had already been studied by algebraists. L. Foissy introduced a noncommutative version of the Connes-Kreimer Hopf algebra, which turns out to be self-dual. Using some homomorphisms defined by the author and W. Zhao, we describe a commutative diagram that relates the aforementioned Hopf algebras to each other and to the Hopf algebras of symmetric functions, noncommutative symmetric functions, and quasi-symmetric functions.
Keywords
Cite
@article{arxiv.0812.2419,
title = {Rooted trees and symmetric functions: Zhao's homomorphism and the commutative hexagon},
author = {Michael E. Hoffman},
journal= {arXiv preprint arXiv:0812.2419},
year = {2009}
}
Comments
For International Conference on Vertex Operator Algebras and Related Fields (Normal, IL, 2008)