{
  "id": "2011.05220",
  "version": "v1",
  "published": "2020-11-10T16:25:29.000Z",
  "updated": "2020-11-10T16:25:29.000Z",
  "title": "Relations Between the Strong Global Dimension, Complexes of Fized Size and Derived Category",
  "authors": [
    "Y. Calderón-Henao",
    "F. Gallego-Olaya",
    "H. Giraldo"
  ],
  "comment": "16 pages and 4 figures",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $\\mathbb{Z}$ be the integer numbers, $\\mathbb{K}$ an algebraically closed field, $\\Lambda$ a finite dimensional $\\mathbb{K}$-algebra, mod$\\Lambda$ the category of finitely generated right modules, proj$\\Lambda$ the full subcategory of mod$\\Lambda$ consisting of all projective $\\Lambda$-modules, and $C_n(proj\\Lambda)$ the bounded complexes of projective $\\Lambda$-modules of fixed size for any integer $n\\geq2$. We find an algorithm to calculate the strong global dimension of $\\Lambda$, when $\\Lambda$ is a finite strong global dimension and derived discrete, using the Auslander-Reiten quivers of the categories $C_n(proj\\Lambda)$. Also, we show the relation between the Auslander-Reiten quiver of the bounded derived category $D^b(\\Lambda)$ and the Auslander-Reiten quiver of $C_{\\eta+1}(proj\\Lambda)$, where $\\eta=s.gl.dim(\\Lambda)$ (strong global dimension of $\\Lambda$).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-10T16:25:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18Gxx",
      "F.2.2"
    ],
    "keywords": [
      "derived category",
      "auslander-reiten quiver",
      "fized size",
      "finite strong global dimension",
      "full subcategory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}