{
  "id": "1104.0399",
  "version": "v1",
  "published": "2011-04-03T16:10:04.000Z",
  "updated": "2011-04-03T16:10:04.000Z",
  "title": "Complex structure of a real Clifford algebra",
  "authors": [
    "Jason Hanson"
  ],
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "The classification of real Clifford algebras in terms of matrix algebras is well--known. Here we consider the real Clifford algebra ${\\mathcal Cl}(r,s)$ not as a matrix algebra, but as a Clifford module over itself. We show that ${\\mathcal Cl}(r,s)$ possesses a basis independent complex structure only when the square of the volume element $\\omega$ is -1, in which case it is uniquely given up to sign by right multiplication with $\\omega$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-04-03T16:10:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A66"
    ],
    "keywords": [
      "real clifford algebra",
      "matrix algebra",
      "basis independent complex structure",
      "clifford module",
      "volume element"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1104.0399H"
    }
  }
}