Rooted trees and symmetric functions: Zhao's homomorphism and the commutative hexagon

Details Rooted trees and symmetric functions: Zhao's homomorphism and the commutative hexagon Rooted trees and symmetric functions: Zhao's homomorphism and the commutative hexagon

2008-12-12

arxiv.org/abs/0812.2419v1

in Vertex Operator Algebras and Related Areas, M. Bergvelt et. al. (eds.), AMS, Providence, 2009, pp. 85-95

Mathematics

Quantum Algebra

For International Conference on Vertex Operator Algebras and Related Fields (Normal, IL, 2008)

Scientific paper

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.

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