{
  "id": "1603.06490",
  "version": "v1",
  "published": "2016-03-21T16:46:09.000Z",
  "updated": "2016-03-21T16:46:09.000Z",
  "title": "Derived categories of quasi-hereditary algebras and their derived composition series",
  "authors": [
    "Martin Kalck"
  ],
  "comment": "35 pages, to appear in Proc. of Conference of the DFG priority program on Representation Theory, Bad Honnef, March 2015, comments are welcome!",
  "categories": [
    "math.RT"
  ],
  "abstract": "We study composition series of derived module categories in the sense of Angeleri H\\\"ugel, K\\\"onig & Liu for quasi-hereditary algebras. More precisely, we show that having a composition series with all factors being derived categories of vector spaces does not characterise derived categories of quasi-hereditay algebras. This gives a negative answer to a question of Liu & Yang and the proof also confirms part of a conjecture of Bobi\\'nski & Malicki. In another direction, we show that derived categories of quasi-hereditary algebras can have composition series with lots of different lengths and composition factors. In other words, there is no Jordan-H\\\"older property for composition series of derived categories of quasi-hereditary algebras.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-21T16:46:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18E30",
      "16G20"
    ],
    "keywords": [
      "quasi-hereditary algebras",
      "derived composition series",
      "study composition series",
      "vector spaces",
      "confirms part"
    ],
    "tags": [
      "conference paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160306490K"
    }
  }
}