{
  "id": "1302.1730",
  "version": "v1",
  "published": "2013-02-07T12:36:37.000Z",
  "updated": "2013-02-07T12:36:37.000Z",
  "title": "Subalgebra depths within the path algebra of an acyclic quiver",
  "authors": [
    "Lars Kadison",
    "Christopher J. Young"
  ],
  "comment": "14 pp. to appear in Proceedings A.G.M.P. Conf. Mulhouse, 2011, Springer",
  "categories": [
    "math.RT"
  ],
  "abstract": "Constraints are given on the depth of diagonal subalgebras in generalized triangular matrix algebras. The depth of the top subalgebra B = A /rad A in a finite, connected, acyclic quiver algebra A over an algebraically closed field K is then computed. Also the depth of the primary arrow subalgebra 1K + rad A = B in A is obtained. The two types of subalgebras have depths 3 and 4 respectively, independent of the number of vertices. An upper bound on depth is obtained for the quotient of a subalgebra pair.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-02-07T12:36:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "path algebra",
      "subalgebra depths",
      "primary arrow subalgebra 1k",
      "generalized triangular matrix algebras",
      "acyclic quiver algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.1730K"
    }
  }
}