{
  "id": "math/0209088",
  "version": "v1",
  "published": "2002-09-09T12:46:55.000Z",
  "updated": "2002-09-09T12:46:55.000Z",
  "title": "E-theory is a special case of KK-theory",
  "authors": [
    "Vladimir Manuilov",
    "Klaus Thomsen"
  ],
  "comment": "22 pages, LaTeX",
  "categories": [
    "math.OA"
  ],
  "abstract": "Let A and B be $C^*$-algebras, A separable, and B $\\sigma$-unital and stable. It is shown that there are natural isomorphisms $E(A,B)=KK(SA,Q(B))=[SA,Q(B)\\otimes K]$, where $SA=C_0(0,1)\\otimes A$, $[\\cdot,\\cdot]$ denotes the set of homotopy classes of *-homomorphisms, $Q(B) = M(B)/B$ is the generalized Calkin algebra and K denotes the $C^*$-algebra of compact operators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-09-09T12:46:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "special case",
      "natural isomorphisms",
      "homotopy classes",
      "generalized calkin algebra",
      "compact operators"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......9088M"
    }
  }
}