{
  "id": "1311.1258",
  "version": "v3",
  "published": "2013-11-06T00:33:09.000Z",
  "updated": "2015-07-29T05:43:38.000Z",
  "title": "Derived equivalences between triangular matrix algebras",
  "authors": [
    "Liping Li"
  ],
  "comment": "Big revision made",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "In this paper we study derived equivalences between triangular matrix algebras using certain classical recollements. We show that special properties of these recollements actually characterize triangular matrix algebras, and describe methods to construct tilting modules and tilting complexes inducing derived equivalences between them.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-12-06T04:12:09.000Z",
      "title": "Triangular Matrix Algebras: Recollements, Torsion Theories, and Derived equivalences",
      "abstract": "In this paper we study representations and homological properties of finite dimensional triangular matrix algebras, focusing on recollements, torsion theories, and derived equivalences. We construct certain recollements and torsion theories whose specific properties actually characterize triangular matrix algebras, and describe methods to construct tilting modules and tilting complexes. We prove that these tilting objects induce derived equivalences between triangular matrix algebras.",
      "comment": "Proof simplified; new results and references added",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-07-29T05:43:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G10",
      "16E35"
    ],
    "keywords": [
      "torsion theories",
      "recollements",
      "finite dimensional triangular matrix algebras",
      "characterize triangular matrix algebras",
      "tilting objects induce derived equivalences"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.1258L"
    }
  }
}