{
  "id": "2212.10106",
  "version": "v1",
  "published": "2022-12-20T09:27:59.000Z",
  "updated": "2022-12-20T09:27:59.000Z",
  "title": "Symmetries of $\\mathfrak{gl}_N$-foams",
  "authors": [
    "You Qi",
    "Louis-Hadrien Robert",
    "Joshua Sussan",
    "Emmanuel Wagner"
  ],
  "comment": "34 pages, many figures. Comments welcome!",
  "categories": [
    "math.GT",
    "math.QA",
    "math.RT"
  ],
  "abstract": "We give an action of a Lie subalgebra of the Witt algebra on foams. This action is compatible with the $\\mathfrak{gl}_N$-foam evaluation formula. In particular, this endows states spaces associated with $\\mathfrak{gl}_N$-webs with an $\\mathfrak{sl}_2$-action. When working in positive characteristic, this can be used to define a $p$-DG structure on these state spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-20T09:27:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K16",
      "17B10",
      "18N25",
      "18G35",
      "57K18"
    ],
    "keywords": [
      "symmetries",
      "foam evaluation formula",
      "endows states spaces",
      "witt algebra",
      "state spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}