{
  "id": "0704.1803",
  "version": "v3",
  "published": "2007-04-13T17:45:01.000Z",
  "updated": "2007-08-22T20:32:23.000Z",
  "title": "Regularity properties in the classification program for separable amenable C*-algebras",
  "authors": [
    "George A. Elliott",
    "Andrew S. Toms"
  ],
  "comment": "19 pages, to appear in Bull. AMS, April 2008",
  "categories": [
    "math.OA",
    "math.FA"
  ],
  "abstract": "We report on recent progress in the program to classify separable amenable C*-algebras. Our emphasis is on the newly apparent role of regularity properties such as finite decomposition rank, strict comparison of positive elements, and Z-stability, and on the importance of the Cuntz semigroup. We include a brief history of the program's successes since 1989, a more detailed look at the Villadsen-type algebras which have so dramatically changed the landscape, and a collection of announcements on the structure and properties of the Cuntz semigroup.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2007-08-22T20:32:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46L35",
      "46L80"
    ],
    "keywords": [
      "regularity properties",
      "classification program",
      "separable amenable",
      "cuntz semigroup",
      "finite decomposition rank"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0704.1803E"
    }
  }
}