Rooted trees, Feynman graphs, and Hecke correspondences

Details Rooted trees, Feynman graphs, and Hecke correspondences Rooted trees, Feynman graphs, and Hecke correspondences

2009-09-07

arxiv.org/abs/0909.1139v1

Mathematics

Quantum Algebra

Scientific paper

We construct natural representations of the Connes-Kreimer Lie algebras on rooted trees/Feynman graphs arising from Hecke correspondences in the categories $\LRF, \LFG$ constructed by K. Kremnizer and the author. We thus obtain the insertion/elimination representations constructed by Connes-Kreimer as well as an isomorphic pair we term top-insertion/top-elimination. We also construct graded finite-dimensional sub/quotient representations of these arising from "truncated" correspondences.

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