{
  "id": "2002.05718",
  "version": "v1",
  "published": "2020-02-13T18:59:43.000Z",
  "updated": "2020-02-13T18:59:43.000Z",
  "title": "The universal pre-Lie-Rinehart algebras of aromatic trees",
  "authors": [
    "Gunnar Fløystad",
    "Dominique Manchon",
    "Hans Z. Munthe-Kaas"
  ],
  "comment": "15 pages, 1 figure",
  "categories": [
    "math.RA",
    "cs.NA",
    "math.NA"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-13T18:59:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "universal pre-lie-rinehart algebras",
      "flat torsion-free lie-rinehart algebra",
      "natural trace map",
      "organize colored aromatic trees",
      "algebraic foundations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}