{
  "id": "0911.1100",
  "version": "v2",
  "published": "2009-11-05T18:54:03.000Z",
  "updated": "2011-02-08T06:06:49.000Z",
  "title": "Universal deformation rings of modules over Frobenius algebras",
  "authors": [
    "Frauke M. Bleher",
    "Jose A. Velez-Marulanda"
  ],
  "comment": "25 pages, 2 figures. Some typos have been fixed, the outline of the paper has been changed to improve readability",
  "journal": "J. Algebra 367 (2012), 176-202",
  "doi": "10.1016/j.jalgebra.2012.06.008",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $k$ be a field, and let $\\Lambda$ be a finite dimensional $k$-algebra. We prove that if $\\Lambda$ is a self-injective algebra, then every finitely generated $\\Lambda$-module $V$ whose stable endomorphism ring is isomorphic to $k$ has a universal deformation ring $R(\\Lambda,V)$ which is a complete local commutative Noetherian $k$-algebra with residue field $k$. If $\\Lambda$ is also a Frobenius algebra, we show that $R(\\Lambda,V)$ is stable under taking syzygies. We investigate a particular Frobenius algebra $\\Lambda_0$ of dihedral type, as introduced by Erdmann, and we determine $R(\\Lambda_0,V)$ for every finitely generated $\\Lambda_0$-module $V$ whose stable endomorphism ring is isomorphic to $k$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-02-08T06:06:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G20",
      "20C20"
    ],
    "keywords": [
      "universal deformation ring",
      "frobenius algebra",
      "complete local commutative noetherian",
      "stable endomorphism ring",
      "isomorphic"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0911.1100B"
    }
  }
}