{
  "id": "math/0302335",
  "version": "v2",
  "published": "2003-02-26T21:16:50.000Z",
  "updated": "2003-02-28T17:59:25.000Z",
  "title": "Real C*-algebras, United KK-theory, and the Universal Coefficient Theorem",
  "authors": [
    "Jeffrey L. Boersema"
  ],
  "comment": "42 pages; correction to abstract: the correct hypothesis is that the complexification of A (not B) is in the bootstrap category",
  "categories": [
    "math.OA"
  ],
  "abstract": "We define united KK-theory for real C*-algebras A and B such that A is separable and B is sigma-unital, extending united K-theory in the sense that KK\\crt(\\R, B) = K\\crt(B). United KK-theory contains real, complex, and self-conjugate KK-theory; but unlike unaugmented real KK-theory, it admits a universal coefficient theorem. For all separable A and B in which the complexification of A is in the bootstrap category, KK\\crt(A,B) can be written as the middle term of a short exact sequence whose outer terms involve the united K-theory of A and B. As a corollary, we prove that united K-theory classifies KK-equivalence for real C*-algebras whose complexification is in the bootstrap category.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2003-02-28T17:59:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46L80",
      "19K35",
      "46M18"
    ],
    "keywords": [
      "universal coefficient theorem",
      "bootstrap category",
      "united kk-theory contains real",
      "short exact sequence",
      "united k-theory classifies kk-equivalence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......2335B"
    }
  }
}