{
  "id": "2301.02517",
  "version": "v1",
  "published": "2023-01-06T14:10:40.000Z",
  "updated": "2023-01-06T14:10:40.000Z",
  "title": "The Critical Groups of Adinkras up to 2-Rank of Cayley Graphs",
  "authors": [
    "Chi Ho Yuen"
  ],
  "comment": "8 pages, 1 figure",
  "categories": [
    "math.CO",
    "math.RA"
  ],
  "abstract": "Adinkras are graphical gadgets introduced by physicists to study supersymmetry, which can be thought of as the Cayley graphs for supersymmetry algebras. Improving the result of Iga et al., we determine the critical group of an Adinkra given the 2-rank of the Laplacian of the underlying Cayley graph. As a corollary, we show that the critical group is independent of the signature of the Adinkra. The proof uses the monodromy pairing on these critical groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-06T14:10:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50",
      "05C22",
      "05E30",
      "14H40",
      "15B36"
    ],
    "keywords": [
      "critical group",
      "cayley graph",
      "study supersymmetry",
      "supersymmetry algebras",
      "physicists"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}