{
  "id": "2305.01103",
  "version": "v1",
  "published": "2023-05-01T22:00:16.000Z",
  "updated": "2023-05-01T22:00:16.000Z",
  "title": "Relations Between the Strong Global dimension, Complexes of Fixed Size and Derived Category",
  "authors": [
    "Yohny Calderón-Henao",
    "Felipe Gallego-Olaya",
    "Hernán Giraldo"
  ],
  "comment": "20 pages and 3 figures. arXiv admin note: substantial text overlap with arXiv:2011.05220",
  "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 found an algorithm to calculate the strong global dimension of $\\Lambda$, when $\\Lambda$ has 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": "2023-05-01T22:00:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "derived category",
      "fixed size",
      "auslander-reiten quiver",
      "finite strong global dimension",
      "full subcategory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}