{
  "id": "1808.02092",
  "version": "v1",
  "published": "2018-08-06T20:09:37.000Z",
  "updated": "2018-08-06T20:09:37.000Z",
  "title": "Tame hereditary path algebras and amenability",
  "authors": [
    "Sebastian Eckert"
  ],
  "comment": "13 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "In this note we are concerned with the notion of amenable representation type as defined in a recent paper by G\\'abor Elek. Roughly speaking, an algebra is of amenable type if for all $\\varepsilon > 0$, every finite-dimensional module has a submodule which is a direct sum of modules which are small with respect to $\\varepsilon$ such that the quotient is also small in that respect. We will show that the tame hereditary path algebras of quivers of extended Dynkin type over any field $k$ are of amenable type, thus extending a conjecture in the aforementioned paper to another class of tame algebras. In doing so, we avoid using already known results for string algebras.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-06T20:09:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G20",
      "16G60"
    ],
    "keywords": [
      "tame hereditary path algebras",
      "amenability",
      "amenable type",
      "direct sum",
      "tame algebras"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}