{
  "id": "2110.08606",
  "version": "v2",
  "published": "2021-10-16T16:30:30.000Z",
  "updated": "2022-12-28T05:18:31.000Z",
  "title": "Lattices of t-structures and thick subcategories for discrete cluster categories",
  "authors": [
    "Sira Gratz",
    "Alexandra Zvonareva"
  ],
  "comment": "21 pages, comments welcome",
  "categories": [
    "math.RT",
    "math.CT"
  ],
  "abstract": "We classify t-structures and thick subcategories in discrete cluster categories $\\mathcal{C}(\\mathcal{Z})$ of Dynkin type $A$, and show that the set of all t-structures on $\\mathcal{C}(\\mathcal{Z})$ is a lattice under inclusion of aisles, with meet given by their intersection. We show that both the lattice of t-structures on $\\mathcal{C}(\\mathcal{Z})$ obtained in this way and the lattice of thick subcategories of $\\mathcal{C}(\\mathcal{Z})$ are intimately related to the lattice of non-crossing partitions of type $A$. In particular, the lattice of equivalence classes of non-degenerate t-structures on such a category is isomorphic to the lattice of non-crossing partitions of a finite linearly ordered set.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-12-28T05:18:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18E40",
      "06A12"
    ],
    "keywords": [
      "discrete cluster categories",
      "thick subcategories",
      "non-crossing partitions",
      "finite linearly ordered set",
      "equivalence classes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}