{
  "id": "2311.14394",
  "version": "v1",
  "published": "2023-11-24T10:22:09.000Z",
  "updated": "2023-11-24T10:22:09.000Z",
  "title": "Odd Khovanov homology and higher representation theory",
  "authors": [
    "Léo Schelstraete",
    "Pedro Vaz"
  ],
  "comment": "60 pages, multiple colored figures, comments welcome!",
  "categories": [
    "math.GT",
    "math.QA",
    "math.RT"
  ],
  "abstract": "We define a supercategorification of the $q$-Schur algebra of level two and an odd analogue of $\\mathfrak{gl}_2$-foams. Using these constructions, we define a homological invariant of tangles, and show that it coincides with odd Khovanov homology when restricted to links. This gives a representation theoretic construction of odd Khovanov homology. In the process, we define a tensor product on the category of chain complexes in super-2-categories which is compatible with homotopies. This could be of independent interest.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-24T10:22:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "odd khovanov homology",
      "higher representation theory",
      "representation theoretic construction",
      "odd analogue",
      "schur algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 60,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}