{
  "id": "0807.4988",
  "version": "v3",
  "published": "2008-07-31T06:17:50.000Z",
  "updated": "2010-01-19T03:34:14.000Z",
  "title": "C*-Algebra Relations",
  "authors": [
    "Terry A. Loring"
  ],
  "comment": "Added a few examples. 24 pages",
  "journal": "Math. Scand. 107 (2010), no. 1, 43-72",
  "categories": [
    "math.OA"
  ],
  "abstract": "We investigate relations on elements in C*-algebras, including *-polynomial relations, order relations and all relations that correspond to universal C*-algebras. We call these C*-relations and define them axiomatically. Within these are the compact C*-relations, which are those that determine universal C*-algebras, and we introduce the more flexible concept of a closed C*-relation. In the case of a finite set of generators, we show that closed C*-relations correspond to the zero-sets of elements in a free sigma -C*-algebra. This provides a solid link between two of the previous theories on relations in C*-algebras. Applications to lifting problems are briefly considered in the last section.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-01-19T03:34:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46L05",
      "46L85"
    ],
    "keywords": [
      "finite set",
      "solid link",
      "order relations",
      "correspond",
      "free sigma"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0807.4988L"
    }
  }
}