A nondiagrammatic description of the Connes-Kreimer Hopf algebra. (Q1946181)

An alternative description of the Connes-Kreimer Hopf algebra of Feynman graphs is constructed. First, on the dual level, one constructs a pre-Lie algebra of polynomial vector fields, invariant under the action of an orthogonal group. It is proved that it contains a pre-Lie subalgebra isomorphic to the pre-Lie algebra of Feynman graphs, with the help of chord diagrams. Dually, one obtains a description of the Hopf algebra of Feynman graphs in terms of tensors.