{
  "id": "1208.6424",
  "version": "v2",
  "published": "2012-08-31T08:53:13.000Z",
  "updated": "2012-10-16T20:01:56.000Z",
  "title": "Cellular structure of $q$-Brauer algebras",
  "authors": [
    "Dung Tien Nguyen"
  ],
  "doi": "10.1007/s10468-013-9452-9",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "In this paper we consider the $q$-Brauer algebra over $R$ a commutative noetherian domain. We first construct a new basis for $q$-Brauer algebras, and we then prove that it is a cell basis, and thus these algebras are cellular in the sense of Graham and Lehrer. In particular, they are shown to be an iterated inflation of Hecke algebras of type $A_{n-1}.$ Moreover, when $R$ is a field of arbitrary characteristic, we determine for which parameters the $q$-Brauer algebras are quasi-heredity. So the general theory of cellular algebras and quasi-hereditary algebras applies to $q$-Brauer algebras. As a consequence, we can determine all irreducible representations of $q$-Brauer algebras by linear algebra methods.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-10-16T20:01:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G30"
    ],
    "keywords": [
      "brauer algebra",
      "cellular structure",
      "quasi-hereditary algebras applies",
      "linear algebra methods",
      "cell basis"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.6424T"
    }
  }
}