{
  "id": "1511.08081",
  "version": "v1",
  "published": "2015-11-25T15:09:19.000Z",
  "updated": "2015-11-25T15:09:19.000Z",
  "title": "Deformations of complexes for finite dimensional algebras",
  "authors": [
    "Frauke M. Bleher",
    "Jose A. Velez-Marulanda"
  ],
  "comment": "29 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $k$ be a field and let $\\Lambda$ be a finite dimensional $k$-algebra. We prove that every bounded complex $V^\\bullet$ of finitely generated $\\Lambda$-modules has a well-defined versal deformation ring $R(\\Lambda,V^\\bullet)$ which is a complete local commutative Noetherian $k$-algebra with residue field $k$. We also prove that certain nice two-sided tilting complexes between $\\Lambda$ and another finite dimensional $k$-algebra $\\Gamma$ preserve these versal deformation rings. We apply these results to the derived equivalence class of a particular family of algebras of dihedral type which were introduced by Erdmann and shown by Holm to be not derived equivalent to any block of a group algebra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-25T15:09:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G10",
      "16G20",
      "20C20"
    ],
    "keywords": [
      "finite dimensional algebras",
      "versal deformation ring",
      "complete local commutative noetherian",
      "well-defined versal deformation",
      "nice two-sided tilting complexes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151108081B"
    }
  }
}