{
  "id": "2312.08390",
  "version": "v1",
  "published": "2023-12-12T12:58:30.000Z",
  "updated": "2023-12-12T12:58:30.000Z",
  "title": "Khovanov algebras for the periplectic Lie superalgebras",
  "authors": [
    "Jonas Nehme"
  ],
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "The periplectic Lie superalgebra $\\mathfrak{p}(n)$ is one of the most mysterious and least understood simple classical Lie superalgebras with reductive even part. We approach the study of its finite dimensional representation theory in terms of Schur--Weyl duality. We provide an idempotent version of its centralizer, i.e. the super Brauer algebra. We use this to describe explicitly the endomorphism ring of a projective generator for $\\mathfrak{p}(n)$ resembling the Khovanov algebra of [BS11a]. We also give a diagrammatic description of the translation functors from [BDE19] in terms of certain bimodules and study their effect on projective, standard, costandard and irreducible modules. These results will be used to classify irreducible summands in $V^{\\otimes d}$, compute $\\mathrm{Ext}^1$ between irreducible modules and show that $\\mathfrak{p}(n)$-mod does not admit a Koszul grading.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-12T12:58:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10"
    ],
    "keywords": [
      "periplectic lie superalgebra",
      "khovanov algebra",
      "understood simple classical lie superalgebras",
      "finite dimensional representation theory",
      "super brauer algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}