{
  "id": "1501.01461",
  "version": "v1",
  "published": "2015-01-07T12:18:05.000Z",
  "updated": "2015-01-07T12:18:05.000Z",
  "title": "On a question of rickard on tensor product of stably equivalent algebras",
  "authors": [
    "Serge Bouc",
    "Alexander Zimmermann"
  ],
  "categories": [
    "math.GR",
    "math.CT",
    "math.RA",
    "math.RT"
  ],
  "abstract": "Let F be the algebraic closure of the prime field of characteristic p. After observing that the principal block B of F PSU (3, p^ r) is stably equivalent of Morita type to its Brauer correspondent b, we show however that the centre of B is not isomorphic as an algebra to the centre of b in the cases (p, r) $\\in$ {(2, 2), (3, 1), (5, 1)}. As a consequence, the algebra B $\\otimes$ F[X]/X^p is not stably equivalent of Morita type to b $\\otimes$ F[X]/X^p in these cases. This yields a negative answer to a question of Rickard.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-07T12:18:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stably equivalent algebras",
      "tensor product",
      "morita type",
      "principal block",
      "brauer correspondent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150101461B"
    }
  }
}