{
  "id": "1701.08411",
  "version": "v1",
  "published": "2017-01-29T18:04:43.000Z",
  "updated": "2017-01-29T18:04:43.000Z",
  "title": "A cellular algebra with specific decomposition of the unity",
  "authors": [
    "Mufida M. Hmaida"
  ],
  "comment": "10pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $ \\mathbb{A}$ be a cellular algebra over a field $\\mathbb{F}$ with a decomposition of the identity $ 1_{\\mathbb{A}} $ into orthogonal idempotents $ e_i$, $i \\in I$ (for some finite set $I$) satisfying some properties. We describe the entire Loewy structure of cell modules of the algebra $ \\mathbb{A} $ by using the representation theory of the algebra $ e_i \\mathbb{A} e_i $ for each $ i $. Moreover, we also study the block theory of $\\mathbb{A}$ by using this decomposition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-29T18:04:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cellular algebra",
      "specific decomposition",
      "entire loewy structure",
      "representation theory",
      "cell modules"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}