{
  "id": "2403.05258",
  "version": "v1",
  "published": "2024-03-08T12:29:52.000Z",
  "updated": "2024-03-08T12:29:52.000Z",
  "title": "Some homological properties of category $\\mathcal{O}$, VII",
  "authors": [
    "Volodymyr Mazorchuk"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "We describe Calabi-Yau objects in the regular block of the (parabolic) BGG category $\\mathcal{O}$ associated to a semi-simple finite dimensional complex Lie algebra. Each such object comes with a natural transformation from the Serre functor to a shifted identity whose evaluation at that object is an isomorphism.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-08T12:29:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "homological properties",
      "finite dimensional complex lie algebra",
      "semi-simple finite dimensional complex lie",
      "bgg category",
      "serre functor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}