{
  "id": "2001.02164",
  "version": "v1",
  "published": "2020-01-07T16:45:08.000Z",
  "updated": "2020-01-07T16:45:08.000Z",
  "title": "A Decomposition of twisted equivariant K-theory",
  "authors": [
    "José Manuel Gómez",
    "Johana Ramírez"
  ],
  "categories": [
    "math.AT",
    "math.KT"
  ],
  "abstract": "For $G$ a finite group, a normalized 2-cocycle $\\alpha\\in Z^{2}(G,\\mathbb{S}^{1})$ and $X$ a $G$-space on which a normal subgroup $A$ acts trivially, we show that the $\\alpha$-twisted $G$-equivariant $K$-theory of $X$ decomposes as a direct sum of twisted equivariant $K$-theories of $X$ parametrized by the orbits of an action of $G$ on the set of irreducible $\\alpha$-projective representations of $A$. This generalizes the decomposition obtained by G\\'omez and Uribe for equivariant $K$-theory. We also explore some examples of this decomposition for the particular case of the dihedral groups $D_{2n}$ with $n\\ge 1$ an even integer.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-07T16:45:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "twisted equivariant k-theory",
      "decomposition",
      "normal subgroup",
      "finite group",
      "dihedral groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}