{
  "id": "math-ph/0008028",
  "version": "v1",
  "published": "2000-08-22T02:55:25.000Z",
  "updated": "2000-08-22T02:55:25.000Z",
  "title": "Noncommutative Torus from Fibonacci Chains via Foliation",
  "authors": [
    "Hyeong-Chai Jeong",
    "Eunsang Kim",
    "Chang-Yeong Lee"
  ],
  "doi": "10.1088/0305-4470/34/31/201",
  "categories": [
    "math-ph",
    "cond-mat",
    "math.MP"
  ],
  "abstract": "We classify the Fibonacci chains (F-chains) by their index sequences and construct an approximately finite dimensional (AF) $C^*$-algebra on the space of F-chains as Connes did on the space of Penrose tiling. The K-theory on this AF-algebra suggests a connection between the noncommutative torus and the space of F-chains. A noncommutative torus, which can be regarded as the $C^*$-algebra of a foliation on the torus, is explicitly embedded into the AF-algebra on the space of F-chains. As a counterpart of that, we obtain a relation between the space of F-chains and the leaf space of Kronecker foliation on the torus using the cut-procedure of constructing F-chains.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-08-22T02:55:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "noncommutative torus",
      "fibonacci chains",
      "approximately finite dimensional",
      "index sequences",
      "kronecker foliation"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics A Mathematical General",
      "year": 2001,
      "month": "Aug",
      "volume": 34,
      "number": 31
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 540153,
      "adsabs": "2001JPhA...34R...1J"
    }
  }
}