{
  "id": "1211.5622",
  "version": "v5",
  "published": "2012-11-23T22:48:47.000Z",
  "updated": "2013-12-19T07:56:28.000Z",
  "title": "τ-rigid modules for algebras with radical square zero",
  "authors": [
    "Xiaojin Zhang"
  ],
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "In this paper, we show that for an algebra $\\Lambda$ with radical square zero and an indecomposable $\\Lambda$-module $M$ such that $\\Lambda$ is Gorenstein of finite type or $\\tau M$ is $\\tau$-rigid, $M$ is $\\tau$-rigid if and only if the first two projective terms of a minimal projective resolution of $M$ have no on-zero direct summands in common. We also determined all $\\tau$-tilting modules for Nakayama algebras with radical square zero. Moreover, by giving a construction theorem we show that a basic connected radical square zero algebra admitting a unique $\\tau$-tilting module is local.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2013-12-19T07:56:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G10",
      "16G70",
      "16E10"
    ],
    "keywords": [
      "tilting module",
      "connected radical square zero algebra",
      "on-zero direct summands",
      "basic connected radical square zero",
      "radical square zero algebra admitting"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.5622Z"
    }
  }
}