{
  "id": "1902.00317",
  "version": "v1",
  "published": "2019-02-01T13:16:14.000Z",
  "updated": "2019-02-01T13:16:14.000Z",
  "title": "Idempotent reduction for the finitistic dimension conjecture",
  "authors": [
    "Diego Bravo",
    "Charles Paquette"
  ],
  "comment": "9 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "In this note, we prove that if $\\Lambda$ is an Artin algebra with a simple module $S$ of finite projective dimension, then the finiteness of the finitistic dimension of $\\Lambda$ implies that of $(1-e)\\Lambda(1-e)$ where $e$ is the primitive idempotent supporting $S$. We derive some consequences of this. In particular, we recover a result of Green-Solberg-Psaroudakis: if $\\Lambda$ is the quotient of a path algebra by an admissible ideal $I$ whose defining relations do not involve a certain arrow $\\alpha$, then the finitistic dimension of $\\Lambda$ is finite if and only if that of $\\Lambda/\\Lambda\\alpha \\Lambda$ is.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-01T13:16:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16E10",
      "16G20"
    ],
    "keywords": [
      "finitistic dimension conjecture",
      "idempotent reduction",
      "path algebra",
      "finite projective dimension",
      "artin algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}