{
  "id": "2106.05514",
  "version": "v1",
  "published": "2021-06-10T06:09:21.000Z",
  "updated": "2021-06-10T06:09:21.000Z",
  "title": "Symmetric subcategories, tilting modules and derived recollements",
  "authors": [
    "Hongxing Chen",
    "Changchang Xi"
  ],
  "comment": "23 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "For any good tilting module $T$ over a ring $A$, there exists an $n$-symmetric subcategory $\\mathscr{E}$ of a module category such that the derived category of the endomorphism ring of $T$ is a recollement of the derived categories of $\\mathscr{E}$ and $A$ in the sense of Beilinson-Bernstein-Deligne. Thus the kernel of the total left-derived tensor functor induced by the tilting module is triangle equivalent to the derived category of $\\mathscr{E}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-10T06:09:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18E30",
      "16G10",
      "13B30",
      "16S10",
      "13E05"
    ],
    "keywords": [
      "tilting module",
      "symmetric subcategory",
      "derived recollements",
      "derived category",
      "total left-derived tensor functor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}