The necklace Lie coalgebra and renormalization algebras
The necklace Lie coalgebra and renormalization algebras
We give a natural monomorphism from the necklace Lie coalgebra, defined for any quiver, to Connes and Kreimer’s Lie coalgebra of trees, and extend this to a map from a certain quiver-theoretic Hopf algebra to Connes and Kreimer’s renormalization Hopf algebra as well as to pre-Lie versions. These results are …