{
  "id": "2205.11309",
  "version": "v1",
  "published": "2022-05-23T13:51:56.000Z",
  "updated": "2022-05-23T13:51:56.000Z",
  "title": "Derived equivalences of self-injective 2-Calabi--Yau tilted algebras",
  "authors": [
    "Anders S. Kortegaard"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "Consider a $k$-linear Frobenius category $\\mathscr{E}$ with a projective generator such that the corresponding stable category $\\mathscr{C}$ is 2-Calabi--Yau, Hom-finite with split idempotents. Let $l,m\\in\\mathscr{C}$ be maximal rigid objects with self-injective endomorphism algebras. We will show that their endomorphism algebras $\\mathscr{C}(l,l)$ and $\\mathscr{C}(m,m)$ are derived equivalent. Furthermore we will give a description of the two-sided tilting complex which induces this derived equivalence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-23T13:51:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16E35",
      "16G50",
      "18E10",
      "18E30"
    ],
    "keywords": [
      "derived equivalence",
      "tilted algebras",
      "linear frobenius category",
      "maximal rigid objects",
      "self-injective endomorphism algebras"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}