{
  "id": "0811.0926",
  "version": "v3",
  "published": "2008-11-06T12:16:51.000Z",
  "updated": "2010-03-08T23:37:33.000Z",
  "title": "On iterated almost $ν$-stable derived equivalences",
  "authors": [
    "Wei Hu"
  ],
  "comment": "17 pages",
  "categories": [
    "math.RT",
    "math.CT"
  ],
  "abstract": "In a recent paper \\cite{HuXi3}, we introduced a classes of derived equivalences called almost $\\nu$-stable derived equivalences. The most important property is that an almost $\\nu$-stable derived equivalence always induces a stable equivalence of Morita type, which generalizes a well-known result of Rickard: derived-equivalent self-injective algebras are stably equivalent of Morita type. In this paper, we shall consider the compositions of almost $\\nu$-stable derived equivalences and their quasi-inverses, which is called iterated almost $\\nu$-stable derived equivalences. We give a sufficient and necessary condition for a derived equivalence to be an iterated almost $\\nu$-stable derived equivalence, and give an explicit construction of the stable equivalence functor induced by an iterated almost $\\nu$-stable derived equivalence. As a consequence, we get some new sufficient conditions for a derived finite-dimensional algebras to induce a stable equivalence of Morita type.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-03-08T23:37:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18E30",
      "16G10",
      "18G20",
      "16D90"
    ],
    "keywords": [
      "stable derived equivalence",
      "morita type",
      "derived-equivalent self-injective algebras",
      "important property",
      "necessary condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0811.0926H"
    }
  }
}