The necklace Lie coalgebra and renormalization algebras

Details The necklace Lie coalgebra and renormalization algebras The necklace Lie coalgebra and renormalization algebras

2007-02-15

arxiv.org/abs/math-ph/0702055v3

Physics

Mathematical Physics

18 pages, 4 figures: corrected and with new results in v2

Scientific paper

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 direct analogues of Turaev's results in 2004, by replacing algebras of loops on surfaces with algebras of paths on quivers. We also factor the morphism through an algebra of chord diagrams and explain the geometric version. We then explain how all of the Hopf algebras are uniquely determined by the pre-Lie structures, and discuss noncommutative versions of the Hopf algebras.

Affiliated with

Also associated with

No associations

Rating

The necklace Lie coalgebra and renormalization algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The necklace Lie coalgebra and renormalization algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The necklace Lie coalgebra and renormalization algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-302971