{
  "id": "2305.08087",
  "version": "v1",
  "published": "2023-05-14T07:30:42.000Z",
  "updated": "2023-05-14T07:30:42.000Z",
  "title": "$N=2$ supersymmetric structures on classical $W$-algebras",
  "authors": [
    "Eric Ragoucy",
    "Arim Song",
    "Uhi Rinn Suh"
  ],
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We describe an $N=2$ supersymmetric Poisson vertex algebra structure of $N=1$ (resp. $N=0$) classical $W$-algebra associated with $\\mathfrak{sl}(n+1|n)$ and the odd (resp. even) principal nilpotent element. This $N=2$ supersymmetric structure is connected to the principal $\\mathfrak{sl}(2|1)$-embedding in $\\mathfrak{sl}(n+1|n)$ superalgebras, which are the only basic Lie superalgebras that admit such a principal embedding.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-14T07:30:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "supersymmetric structure",
      "supersymmetric poisson vertex algebra structure",
      "principal nilpotent element",
      "basic lie superalgebras"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}