{
  "id": "1405.5903",
  "version": "v2",
  "published": "2014-05-22T20:36:35.000Z",
  "updated": "2015-09-11T08:26:27.000Z",
  "title": "Blocks of the Grothendieck ring of equivariant bundles on a finite group",
  "authors": [
    "Cédric Bonnafé"
  ],
  "comment": "8 pages",
  "categories": [
    "math.RT",
    "math.GR"
  ],
  "abstract": "If $G$ is a finite group, the Grothendieck group ${\\mathbf{K}}\\_G(G)$ of the category of $G$-equivariant ${\\mathbb{C}}$-vector bundles on $G$ (for the action of $G$ on itself by conjugation) is endowed with a structure of (commutative) ring. If $K$ is a sufficiently large extension of ${\\mathbb{Q}}\\_{\\! p}$ and ${\\mathcal{O}}$ denotes the integral closure of ${\\mathcal{Z}}\\_{\\! p}$ in $K$, the $K$-algebra $K{\\mathbf{K}}\\_G(G)=K \\otimes\\_{\\mathbb{Z}} {\\mathbf{K}}\\_G(G)$ is split semisimple. The aim of this paper is to describe the ${\\mathcal{O}}$-blocks of the ${\\mathcal{O}}$-algebra ${\\mathcal{O}} {\\mathbf{K}}\\_G(G)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-22T20:36:35.000Z",
      "abstract": "If $G$ is a finite group, the Grothendieck group $\\Kb_G(G)$ of the category of $G$-equivariant $\\CM$-vector bundles on $G$ (for the action of $G$ on itself by conjugation) is endowed with a structure of (commutative) ring. If $K$ is a sufficiently large extension of $\\QM_{\\! p}$ and $\\OC$ denotes the integral closure of $\\ZM_{\\! p}$ in $K$, the $K$-algebra $K\\Kb_G(G)=K \\otimes_\\ZM \\Kb_G(G)$ is split semisimple. The aim of this paper is to describe the $\\OC$-blocks of the $\\OC$-algebra $\\OC \\Kb_G(G)$.",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-09-11T08:26:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite group",
      "equivariant bundles",
      "grothendieck ring",
      "grothendieck group",
      "vector bundles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.5903B"
    }
  }
}