{
  "id": "1705.09621",
  "version": "v1",
  "published": "2017-05-25T13:55:21.000Z",
  "updated": "2017-05-25T13:55:21.000Z",
  "title": "Duality and Serre functor in homotopy categories",
  "authors": [
    "J. Asadollahi",
    "N. Asadollahi",
    "R. Hafezi",
    "R. Vahed"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1605.04745",
  "categories": [
    "math.RT"
  ],
  "abstract": "For a (right and left) coherent ring $A$, we show that there exists a duality between homotopy categories ${\\mathbb{K}}^{{\\rm{b}}}({\\rm mod}{\\mbox{-}}A^{{\\rm op}})$ and ${\\mathbb{K}}^{{\\rm{b}}}({\\rm mod}{\\mbox{-}}A)$. If $A=\\Lambda$ is an artin algebra of finite global dimension, this duality restricts to a duality between their subcategories of acyclic complexes, ${\\mathbb{K}}^{{\\rm{b}}}_{\\rm ac}({\\rm mod}{\\mbox{-}}\\Lambda^{\\rm op})$ and ${\\mathbb{K}}^{{\\rm{b}}}_{\\rm ac}({\\rm mod}{\\mbox{-}}\\Lambda).$ As a result, it will be shown that, in this case, ${\\mathbb{K}}_{\\rm ac}^{{\\rm{b}}}({\\rm mod}{\\mbox{-}}\\Lambda)$ admits a Serre functor and hence has Auslander-Reiten triangles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-25T13:55:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18E30",
      "16E35",
      "18G25"
    ],
    "keywords": [
      "serre functor",
      "homotopy categories",
      "finite global dimension",
      "duality restricts",
      "artin algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}