{
  "id": "1605.09746",
  "version": "v1",
  "published": "2016-05-31T17:59:49.000Z",
  "updated": "2016-05-31T17:59:49.000Z",
  "title": "Universal deformation rings for a class of self-injective special biserial algebras",
  "authors": [
    "Hernan Giraldo",
    "Jose A. Velez-Marulanda"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:1212.5754",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $\\mathbf{k}$ be an algebraically closed field, let $\\Lambda$ be a finite dimensional $\\mathbf{k}$-algebra and let $V$ be a $\\Lambda$-module with stable endomorphism ring isomorphic to $\\mathbf{k}$. If $\\Lambda$ is self-injective then $V$ has a universal deformation ring $R(\\Lambda,V)$, which is a complete local commutative Noetherian $\\mathbf{k}$-algebra with residue field $\\mathbf{k}$. Moreover, if $\\Lambda$ is also a Frobenius $\\mathbf{k}$-algebra then $R(\\Lambda,V)$ is stable under syzygies. We use these facts to determine the universal deformation rings of string $\\Lambda_N$-modules with stable endomorphism ring isomorphic to $\\mathbf{k}$, where $N\\geq 1$ and $\\Lambda_N$ is a self-injective special biserial $\\mathbf{k}$-algebra whose Hochschild cohomology ring is a finitely generated $\\mathbf{k}$-algebra as proved by N. Snashall and R. Taillefer.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-31T17:59:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G10",
      "16G20",
      "20C20"
    ],
    "keywords": [
      "universal deformation ring",
      "self-injective special biserial algebras",
      "stable endomorphism ring isomorphic",
      "complete local commutative noetherian"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}