{
  "id": "1310.2777",
  "version": "v2",
  "published": "2013-10-10T11:32:51.000Z",
  "updated": "2017-05-16T08:41:45.000Z",
  "title": "Brauer-Thrall type theorems for derived module categories",
  "authors": [
    "Chao Zhang",
    "Yang Han"
  ],
  "comment": "23 pages",
  "journal": "Algebr Represent Theor 19(2016), 1369-1386",
  "categories": [
    "math.RT"
  ],
  "abstract": "The numerical invariants (global) cohomological length, (global) cohomological width, and (global) cohomological range of complexes (algebras) are introduced. Cohomological range leads to the concepts of derived bounded algebras and strongly derived unbounded algebras naturally. The first and second Brauer-Thrall type theorems for the bounded derived category of a finite-dimensional algebra over an algebraically closed field are obtained. The first Brauer-Thrall type theorem says that derived bounded algebras are just derived finite algebras. The second Brauer-Thrall type theorem says that an algebra is either derived discrete or strongly derived unbounded, but not both. Moreover, piecewise hereditary algebras and derived discrete algebras are characterized as the algebras of finite global cohomological width and finite global cohomological length respectively.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-10T11:32:51.000Z",
      "title": "Brauer-Thrall type theorems for derived category",
      "comment": "20 pages",
      "journal": null,
      "doi": null,
      "authors": [
        "Yang Han",
        "Chao Zhang"
      ]
    },
    {
      "version": "v2",
      "updated": "2017-05-16T08:41:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "derived category",
      "second brauer-thrall type theorem says",
      "first brauer-thrall type theorem says",
      "global cohomological length",
      "finite global cohomological"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.2777H"
    }
  }
}