{
  "id": "1212.5754",
  "version": "v1",
  "published": "2012-12-23T02:36:35.000Z",
  "updated": "2012-12-23T02:36:35.000Z",
  "title": "Universal deformation rings of string modules over a certain symmetric special biserial algebra",
  "authors": [
    "Jose A. Velez-Marulanda"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $\\k$ be an algebraically closed field, let $\\A$ be a finite dimensional $\\k$-algebra and let $V$ be a $\\A$-module with stable endomorphism ring isomorphic to $\\k$. If $\\A$ is self-injective then $V$ has a universal deformation ring $R(\\A,V)$, which is a complete local commutative Noetherian $\\k$-algebra with residue field $\\k$. Moreover, if $\\Lambda$ is also a Frobenius $\\k$-algebra then $R(\\A,V)$ is stable under syzygies. We use these facts to determine the universal deformation rings of string $\\Ar$-modules whose stable endomorphism ring isomorphic to $\\k$, where $\\Ar$ is a symmetric special biserial $\\k$-algebra that has quiver with relations depending on the four parameters $ \\bar{r}=(r_0,r_1,r_2,k)$ with $r_0,r_1,r_2\\geq 2$ and $k\\geq 1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-12-23T02:36:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G10",
      "16G20",
      "20C20"
    ],
    "keywords": [
      "universal deformation ring",
      "symmetric special biserial algebra",
      "string modules",
      "stable endomorphism ring isomorphic",
      "complete local commutative noetherian"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1212.5754V"
    }
  }
}