{
  "id": "math/0411353",
  "version": "v3",
  "published": "2004-11-16T01:59:21.000Z",
  "updated": "2006-12-20T06:06:37.000Z",
  "title": "$q$-deformation of Witt-Burnside rings",
  "authors": [
    "Young-Tak Oh"
  ],
  "comment": "Some revision was made",
  "categories": [
    "math.RA"
  ],
  "abstract": "In this paper, we construct a $q$-deformation of the Witt-Burnside ring of a profinite group over a commutative ring, where $q$ ranges over the set of integers. When $q=1$, it coincides with the Witt-Burnside ring introduced by A. Dress and C. Siebeneicher (Adv. Math. {70} (1988), 87-132). To achieve our goal we first show that there exists a $q$-deformation of the necklace ring of a profinite group over a commutative ring. As in the classical case, i.e., the case $q=1$, q-deformed Witt-Burnside rings and necklace rings always come equipped with inductions and restrictions. We also study their properties. As a byproduct, we prove a conjecture due to Lenart (J. Algebra. 199 (1998), 703-732). Finally, we classify $\\mathbb W_G^q$ up to strict natural isomorphism in case where $G$ is an abelian profinite group.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2006-12-20T06:06:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F03",
      "11F22",
      "17B70"
    ],
    "keywords": [
      "deformation",
      "strict natural isomorphism",
      "abelian profinite group",
      "necklace ring",
      "q-deformed witt-burnside rings"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....11353O"
    }
  }
}