{
  "id": "2008.12178",
  "version": "v1",
  "published": "2020-08-27T15:13:27.000Z",
  "updated": "2020-08-27T15:13:27.000Z",
  "title": "2-recollements of singualrity categories and Gorenstein defect categories over triangular matrix algebras",
  "authors": [
    "Huanhuan Li",
    "Dandan Yang",
    "Yuefei Zheng",
    "Jiangsheng Hu"
  ],
  "comment": "21 pages, all comments are welcome",
  "categories": [
    "math.RT",
    "math.KT",
    "math.RA"
  ],
  "abstract": "Let $T=(A,M,0,B)$ be a triangular matrix algebra with its corner algebras $A$ and $B$ Artinian and $_AM_B$ an $A$-$B$-bimodule. The 2-recollement structures for singularity categories and Gorenstein defect categories over $T$ are studied. Under mild assumptions, we provide necessary and sufficient conditions for the existences of 2-recollements of singularity categories and Gorenstein defect categories over $T$ relative to those of $A$ and $B$. Parts of our results strengthen and unify the corresponding work in [27,28,34].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-27T15:13:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gorenstein defect categories",
      "triangular matrix algebra",
      "singualrity categories",
      "singularity categories",
      "corner algebras"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}