{
  "id": "2310.13934",
  "version": "v1",
  "published": "2023-10-21T08:07:29.000Z",
  "updated": "2023-10-21T08:07:29.000Z",
  "title": "A generalization of Dugas' construction on stable auto-equivalences for symmetric algebras",
  "authors": [
    "Nengqun Li",
    "Yuming Liu"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "We give a unified generalization of Dugas' construction on stable auto-equivalences of Morita type from local symmetric algebras to arbitrary symmetric algebras. For group algebras $kP$ of $p$-groups in characteristic $p$, we recover all the stable auto-equivalences corresponding to endo-trivial modules over $kP$ except that $P$ is generalized quaternion of order $2^m$. Moreover, we give many examples of stable auto-equivalences of Morita type for non-local symmetric algebras.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-21T08:07:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G10",
      "16D50"
    ],
    "keywords": [
      "stable auto-equivalences",
      "construction",
      "morita type",
      "non-local symmetric algebras",
      "arbitrary symmetric algebras"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}