{
  "id": "2208.00514",
  "version": "v1",
  "published": "2022-07-31T20:43:31.000Z",
  "updated": "2022-07-31T20:43:31.000Z",
  "title": "Post-Lie algebras in Regularity Structures",
  "authors": [
    "Yvain Bruned",
    "Foivos Katsetsiadis"
  ],
  "categories": [
    "math.PR",
    "math.AP",
    "math.RA"
  ],
  "abstract": "In this work, we construct the deformed Butcher-Connes-Kreimer Hopf algebra appearing in Regularity Structures as the universal envelope of a post-Lie algebra. We show that this can be done using either of the two combinatorial structures that have been proposed in the context of singular SPDEs: decorated trees, used in arXiv:1610.0846(8) and multi-indices, used in arXiv:2103.0418(7). Our construction is inspired from arXiv:2103.0418(7) where the Hopf algebra was obtained as the universal envelope of a Lie algebra and the authors showed that one can find a basis that is symmetric with respect to certain elements. We show that this Lie algebra comes from an underlying post-Lie structure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-31T20:43:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "regularity structures",
      "post-lie algebra",
      "universal envelope",
      "lie algebra comes",
      "singular spdes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}