{
  "id": "1004.3943",
  "version": "v1",
  "published": "2010-04-22T15:17:28.000Z",
  "updated": "2010-04-22T15:17:28.000Z",
  "title": "Biserial algebras via subalgebras and the path algebra of D_4",
  "authors": [
    "Julian Külshammer"
  ],
  "doi": "10.1016/j.jalgebra.2010.12.012",
  "categories": [
    "math.RT"
  ],
  "abstract": "We give two new criteria for a basic algebra to be biserial. The first one states that an algebra is biserial iff all subalgebras of the form eAe where e is supported by at most 4 vertices are biserial. The second one gives some condition on modules that must not exist for a biserial algebra. These modules have properties similar to the module with dimension vector (1,1,1,1) for the path algebra of the quiver D_4. Both criteria generalize criteria for an algebra to be Nakayama. They rely on the description of a basic biserial algebra in terms of quiver and relations given by R. Vila-Freyer and W. Crawley- Boevey.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-04-22T15:17:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "path algebra",
      "subalgebras",
      "basic biserial algebra",
      "form eae",
      "basic algebra"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1004.3943K"
    }
  }
}