{
  "id": "2102.01392",
  "version": "v1",
  "published": "2021-02-02T09:07:38.000Z",
  "updated": "2021-02-02T09:07:38.000Z",
  "title": "$τ$-Tilting modules over one-point extensions by a simple module at a source point",
  "authors": [
    "Hanpeng Gao"
  ],
  "comment": "8 pages; accepted by Journal of algebra and its applications",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $B$ be an one-point extension of a finite dimensional $k$-algebra $A$ by a simple $A$-module at a source point $i$. In this paper, we classify the $\\tau$-tilting modules over $B$. Moreover, it is shown that there are equations $$|\\tilt B|=|\\tilt A|+|\\tilt A/\\langle e_i\\rangle|\\quad \\text{and}\\quad |\\stilt B|=2|\\stilt A|+|\\stilt A/\\langle e_i\\rangle|.$$ As a consequence, we can calculate the numbers of $\\tau$-tilting modules and support $\\tau$-tilting modules over linearly Dynkin type algebras whose square radical are zero.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-02T09:07:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G20",
      "16G60"
    ],
    "keywords": [
      "tilting modules",
      "source point",
      "one-point extension",
      "simple module",
      "linearly dynkin type algebras"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}