{
  "id": "1802.01169",
  "version": "v1",
  "published": "2018-02-04T18:04:40.000Z",
  "updated": "2018-02-04T18:04:40.000Z",
  "title": "$τ$-exceptional sequences",
  "authors": [
    "Aslak Bakke Buan",
    "Robert J. Marsh"
  ],
  "comment": "24 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "We introduce the notions of $\\tau$-exceptional and signed $\\tau$-exceptional sequences for any finite dimensional algebra. We prove that for a fixed algebra of rank $n$, and for any positive integer $t \\leq n$, there is a bijection between the set of such sequences of length $t$, and (basic) ordered support $\\tau$-rigid objects with $t$ indecomposable direct summands. If the algebra is hereditary, our notions coincide with exceptional and signed exceptional sequences. The latter were recently introduced by Igusa and Todorov, who constructed a similar bijection in the hereditary setting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-04T18:04:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G20"
    ],
    "keywords": [
      "finite dimensional algebra",
      "similar bijection",
      "notions coincide",
      "hereditary",
      "indecomposable direct summands"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}