{
  "id": "math/0101099",
  "version": "v1",
  "published": "2001-01-11T14:33:55.000Z",
  "updated": "2001-01-11T14:33:55.000Z",
  "title": "Continuous Fields of $C^*$-Algebras Arising from Extensions of Tensor $C^*$-Categories",
  "authors": [
    "Ezio Vasselli"
  ],
  "comment": "28 pages, uses xy.sty, submitted to Journal of Functional Analysis",
  "journal": "Journal of Functional Analysis 199(1) (2003), 122-152",
  "categories": [
    "math.OA"
  ],
  "abstract": "The notion of extension of a given $C^*$-category $C$ by a $C^*$-algebra $A$ is introduced. In the commutative case $A = C(\\Omega)$, the objects of the extension category are interpreted as fiber bundles over $\\Omega$ of objects belonging to the initial category. It is shown that the Doplicher-Roberts algebra (DR-algebra in the following) associated to an object in the extension of a strict tensor $C^*$-category is a continuous field of DR-algebras coming from the initial one. In the case of the category of the hermitian vector bundles over $\\Omega$ the general result implies that the DR-algebra of a vector bundle is a continuous field of Cuntz algebras. Some applications to Pimsner $C^*$-algebras are given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-01-11T14:33:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46L05",
      "14F05",
      "46M05"
    ],
    "keywords": [
      "continuous field",
      "algebras arising",
      "hermitian vector bundles",
      "dr-algebra",
      "general result implies"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 571864,
      "adsabs": "2001math......1099V"
    }
  }
}