Insertion and Elimination: the doubly infinite Lie algebra of Feynman   graphs
  The Lie algebra of Feynman graphs gives rise to two natural representations, acting as derivations on the commutative Hopf algebra of Feynman graphs, by creating or eliminating subgraphs. Insertions and eliminations do not commute, but rather establish a larger Lie algebra of derivations which we here determine. 
Alain Connes and Dirk Kreimer