{
  "id": "1102.2577",
  "version": "v1",
  "published": "2011-02-13T10:41:53.000Z",
  "updated": "2011-02-13T10:41:53.000Z",
  "title": "The finitistic dimension of algebras with a directed stratification]",
  "authors": [
    "Karsten Dietrich"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "We introduce the notion of a directed stratification for a finite-dimensional algebra. For algebras that admit such a stratification we characterise the projective resolutions of finitely generated modules and obtain a result for the finitistic dimension, which is an inductive version of a result of Fossum, Griffith and Reiten. With the developed techniques, which are adopted from the theory of EI-category algebras, we gain deeper insight in the combinatorial nature of this result. A characterisation of algebras which do not admit a directed stratification is given in terms of the Ext-quiver.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-02-13T10:41:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16E10",
      "16G10"
    ],
    "keywords": [
      "directed stratification",
      "finitistic dimension",
      "gain deeper insight",
      "finite-dimensional algebra",
      "ei-category algebras"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1102.2577D"
    }
  }
}