{
  "id": "2401.07474",
  "version": "v1",
  "published": "2024-01-15T05:05:52.000Z",
  "updated": "2024-01-15T05:05:52.000Z",
  "title": "Equivariant Index Theorem on $\\mathbb{R}^n$ in the Context of Continuous Fields of $C^*$-algebras",
  "authors": [
    "Baiying Ren",
    "Hang Wang",
    "Zijing Wang"
  ],
  "categories": [
    "math.OA",
    "math.DG"
  ],
  "abstract": "We prove an equivariant index theorem on the Euclidean space using a continuous field of $C^*$-algebras. This generalizes the work of Elliott, Natsume and Nest, which is a special case of the algebraic index theorem by Nest-Tsygan. Using our formula, the equivariant index of the Bott-Dirac operator on $\\mathbb{R}^{2n}$ can be explicitly calculated.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-15T05:05:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "equivariant index theorem",
      "continuous field",
      "algebraic index theorem",
      "special case",
      "bott-dirac operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}