(Non)Commutative Hopf algebras of trees and (quasi)symmetric functions

Details (Non)Commutative Hopf algebras of trees and (quasi)symmetric functions (Non)Commutative Hopf algebras of trees and (quasi)symmetric functions

2007-10-19

arxiv.org/abs/0710.3739v1

in Renormalization and Galois Theories, A. Connes et. al. (eds.), EMS Publ. House, Zurich, 2009, pp. 209-227

Mathematics

Quantum Algebra

For March 2006 CIRM conference "Renormalization and Galois theories"

Scientific paper

The Connes-Kreimer Hopf algebra of rooted trees, its dual, and the Foissy Hopf algebra of of planar rooted trees are related to each other and to the well-known Hopf algebras of symmetric and quasi-symmetric functions via a pair of commutative diagrams. We show how this point of view can simplify computations in the Connes-Kreimer Hopf algebra and its dual, particularly for combinatorial Dyson-Schwinger equations.

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