{
  "id": "2303.11513",
  "version": "v1",
  "published": "2023-03-21T00:25:53.000Z",
  "updated": "2023-03-21T00:25:53.000Z",
  "title": "Morphisms and extensions between bricks over preprojective algebras of type A",
  "authors": [
    "Eric J. Hanson",
    "Xinrui You"
  ],
  "comment": "24 pages, 11 figures",
  "categories": [
    "math.RT"
  ],
  "abstract": "The bricks over preprojective algebras of type A are known to be in bijection with certain combinatorial objects called \"arcs\". In this paper, we show how one can use arcs to compute bases for the Hom-spaces and first extension spaces between bricks. We then use this description to classify the \"weak exceptional sequences\" over these algebras. Finally, we explain how our result relates to a similar combinatorial model for the exceptional sequences over hereditary algebras of type A.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-21T00:25:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G20",
      "16G10"
    ],
    "keywords": [
      "preprojective algebras",
      "first extension spaces",
      "weak exceptional sequences",
      "similar combinatorial model",
      "result relates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}