{
  "id": "2410.11213",
  "version": "v1",
  "published": "2024-10-15T02:57:24.000Z",
  "updated": "2024-10-15T02:57:24.000Z",
  "title": "$\\mathcal{W}$-absorbing actions of finite groups on the Razak-Jacelon algebra",
  "authors": [
    "Norio Nawata"
  ],
  "comment": "27 pages",
  "categories": [
    "math.OA"
  ],
  "abstract": "We say that a countable discrete group action $\\alpha$ on a C$^*$-algebra $A$ is \\textit{$\\mathcal{W}$-absorbing} if there exist a C$^*$-algebra $B$ and an action $\\beta$ on $B$ such that $\\alpha$ is cocycle conjugate to $\\beta\\otimes \\mathrm{id}_{\\mathcal{W}}$ on $B\\otimes \\mathcal{W}$ where $\\mathcal{W}$ is the Razak-Jacelon algebra. In this paper, we completely classify outer $\\mathcal{W}$-absorbing actions of finite groups on $\\mathcal{W}$ up to conjugacy and cocycle conjugacy.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-15T02:57:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46L55",
      "46L35",
      "46L40"
    ],
    "keywords": [
      "finite groups",
      "razak-jacelon algebra",
      "absorbing actions",
      "countable discrete group action",
      "cocycle conjugate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}