{
  "id": "2004.08251",
  "version": "v1",
  "published": "2020-04-17T14:01:13.000Z",
  "updated": "2020-04-17T14:01:13.000Z",
  "title": "Sufficient and necessary conditions for hereditary of infinite category algebras",
  "authors": [
    "Malte Lackmann",
    "Liping Li"
  ],
  "comment": "Any comments are welcome",
  "categories": [
    "math.RT",
    "math.GR",
    "math.RA"
  ],
  "abstract": "We describe necessary and sufficient conditions for the hereditarity of the category algebra of an infinite EI category satisfying certain combinatorial assumptions. More generally, we discuss conditions such that the left global dimension of a category algebra equals the maximal left global dimension of the endomorphism algebras of its objects, and classify its projective modules in this case. As applications, we completely classify transporter categories, orbit categories, and Quillen categories with left hereditary category algebras over a field.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-17T14:01:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "infinite category algebras",
      "necessary conditions",
      "maximal left global dimension",
      "left hereditary category algebras",
      "category algebra equals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}