{
  "id": "1812.04871",
  "version": "v1",
  "published": "2018-12-12T10:05:08.000Z",
  "updated": "2018-12-12T10:05:08.000Z",
  "title": "Maximal $τ_d$-rigid pairs",
  "authors": [
    "Karin M. Jacobsen",
    "Peter Jorgensen"
  ],
  "comment": "12 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $\\mathscr T$ be a $2$-Calabi--Yau triangulated category, $T$ a cluster tilting object with endomorphism algebra $\\Gamma$. Consider the functor $\\mathscr T( T,- ) : \\mathscr T \\rightarrow \\mod \\Gamma$. It induces a bijection from the isomorphism classes of cluster tilting objects to the isomorphism classes of support $\\tau$-tilting pairs. This is due to Adachi, Iyama, and Reiten. The notion of $( d+2 )$-angulated categories is a higher analogue of triangulated categories. We show a higher analogue of the above result, based on the notion of maximal $\\tau_d$-rigid pairs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-12T10:05:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G10",
      "18E10",
      "18E30",
      "18E35"
    ],
    "keywords": [
      "rigid pairs",
      "cluster tilting object",
      "isomorphism classes",
      "higher analogue",
      "endomorphism algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}