paper

The universal pre-Lie-Rinehart algebras of aromatic trees

arXiv:2002.05718

Abstract

We organize colored aromatic trees into a pre-Lie-Rinehart algebra (i.e. a flat torsion-free Lie-Rinehart algebra) endowed with a natural trace map, and show the freeness of this object among pre-Lie-Rinehart algebras with trace. This yields the algebraic foundations of aromatic B-series.

20 pages, improvements and clarifications added, 1 figure