{
  "id": "1407.2665",
  "version": "v1",
  "published": "2014-07-10T01:23:17.000Z",
  "updated": "2014-07-10T01:23:17.000Z",
  "title": "Top-stable degenerations of finite dimensional representations I",
  "authors": [
    "Birge Huisgen-Zimmermann"
  ],
  "journal": "Proc. London Math. Soc. (3) 96 (2008) 163-198",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "Given a finite dimensional representation $M$ of a finite dimensional algebra, two hierarchies of degenerations of $M$ are analyzed in the context of their natural orders: the poset of those degenerations of $M$ which share the top $M/JM$ with $M$ - here $J$ denotes the radical of the algebra - and the sub-poset of those which share the full radical layering $\\bigl(J^lM/J^{l+1}M\\bigr)_{l \\ge 0}$ with $M$. In particular, the article addresses existence of proper top-stable or layer-stable degenerations - more generally, it addresses the sizes of the corresponding posets including bounds on the lengths of saturated chains - as well as structure and classification.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-10T01:23:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G10",
      "14D20",
      "16D70",
      "16G20"
    ],
    "keywords": [
      "finite dimensional representation",
      "top-stable degenerations",
      "finite dimensional algebra",
      "article addresses existence",
      "natural orders"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.2665H"
    }
  }
}