{
  "id": "1908.02245",
  "version": "v1",
  "published": "2019-08-06T16:33:49.000Z",
  "updated": "2019-08-06T16:33:49.000Z",
  "title": "Gluing support τ-tilting modules over τ-tilting finite algebras",
  "authors": [
    "Yingying Zhang"
  ],
  "comment": "10 pages, comments welcome",
  "categories": [
    "math.RT"
  ],
  "abstract": "The notion of (semi)bricks, regarded as a generalization of (semi)simple modules, appeared in a paper of Ringel in 1976. In recent years, there has been several new developments motivated by links to {\\tau}-tilting theory studied by Demonet-Iyama-Jasso and Asai. In this paper, we will discuss how to glue semibricks along a recollement with the intermediate extension functor similar to gluing simple modules by Beilinson-Bernstein-Deligne. As an application, we investigate the behavior of {\\tau}-tilting finite under recollements of module categories of algebras. Moreover, we give some examples to show the construction of support {\\tau}-tilting modules over {\\tau}-tilting finite algebras by gluing semibricks via recollements.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-06T16:33:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G10",
      "18A22",
      "18A40",
      "18E10"
    ],
    "keywords": [
      "finite algebras",
      "gluing support",
      "intermediate extension functor similar",
      "recollement",
      "module categories"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}