{
  "id": "math/0606647",
  "version": "v1",
  "published": "2006-06-26T14:20:42.000Z",
  "updated": "2006-06-26T14:20:42.000Z",
  "title": "Auslander-Reiten triangles in subcategories",
  "authors": [
    "Peter Jorgensen"
  ],
  "comment": "19 pages",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "This paper introduces Auslander-Reiten triangles in subcategories of triangulated categories. The main theorem of the paper shows that there is a close connection with covers and envelopes, also known as minimal right- and left-approximations. Namely, under suitable assumptions, if M is an object in the subcategory C of the triangulated category T and X --> Y --> M --> is an Auslander-Reiten triangle in T, then there is an Auslander-Reiten triangle K --> L --> M --> in C if and only if there is a C-cover of the form K --> X. The main theorem is used to give a new proof of the existence of Auslander-Reiten sequences over finite dimensional algebras.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-06-26T14:20:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G70",
      "18E30"
    ],
    "keywords": [
      "auslander-reiten triangle",
      "subcategory",
      "main theorem",
      "triangulated category",
      "finite dimensional algebras"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......6647J"
    }
  }
}