{
  "id": "0803.0252",
  "version": "v1",
  "published": "2008-03-03T15:08:19.000Z",
  "updated": "2008-03-03T15:08:19.000Z",
  "title": "Secondary multiplication in Tate cohomology of certain p-groups",
  "authors": [
    "Martin Langer"
  ],
  "comment": "35 pages",
  "categories": [
    "math.AT",
    "math.GR"
  ],
  "abstract": "Let k be a field and let G be a finite group. By a theorem of D.Benson, H.Krause and S.Schwede, there is a canonical element in the Hochschild cohomology of the Tate cohomology HH^{3,-1} H*G with the following property: Given any graded H*G-module X, the image of the canonical element in Ext^{3,-1}(X,X) is zero if and only if X is isomorphic to a direct summand of H*(G,M) for some kG-module M. We investigate this canonical element in certain special cases, namely that of (finite) abelian p-groups and the quaternion group. In case of non-triviality of the canonical element, we also give examples of non-realizable modules X.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-03-03T15:08:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20J06",
      "55S35"
    ],
    "keywords": [
      "tate cohomology",
      "secondary multiplication",
      "canonical element",
      "finite group",
      "quaternion group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0803.0252L"
    }
  }
}