{
  "id": "1608.01616",
  "version": "v1",
  "published": "2016-08-04T17:16:23.000Z",
  "updated": "2016-08-04T17:16:23.000Z",
  "title": "Projective Dimensions and Extensions of Modules from Titled to Cluster-Tilted Algebras",
  "authors": [
    "Stephen Zito"
  ],
  "comment": "20 pages. arXiv admin note: text overlap with arXiv:1410.1732, arXiv:1604.06907 by other authors",
  "categories": [
    "math.RT"
  ],
  "abstract": "We study the module categories of a tilted algebra C and the corresponding cluster-tilted algebra B. We investigate how various properties of a C-module are affected when considered in the module category of B. We give a complete classification of the projective dimension of a C-module inside the module category of B. If a C-module M is rigid, we show two sufficient conditions for M to be a rigid B-module. In particular, if M is an indecomposable and rigid C-module, we prove M is always a rigid B-module.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-04T17:16:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G20",
      "16G70"
    ],
    "keywords": [
      "projective dimension",
      "module category",
      "rigid b-module",
      "extensions",
      "c-module inside"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}