{
  "id": "2411.07910",
  "version": "v1",
  "published": "2024-11-12T16:34:59.000Z",
  "updated": "2024-11-12T16:34:59.000Z",
  "title": "Projective resolutions of simple modules and Hochschild cohomology for incidence algebras",
  "authors": [
    "Viktor Bekkert",
    "John William MacQuarrie",
    "Júlio Marques"
  ],
  "comment": "14 pages",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "We give an efficient algorithmic method to calculate minimal projective resolutions of simple modules for a finite dimensional incidence $k$-algebra $\\Lambda$, where $k$ is a field. We apply the method to the calculation of $Ext$-groups between simple $\\Lambda$-modules, Hochschild cohomology groups $HH^i(\\Lambda, \\Lambda)$, and singular cohomology groups of finite $T_0$ topological spaces with coefficients in $k$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-11-12T16:34:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16E40",
      "16G20"
    ],
    "keywords": [
      "simple modules",
      "incidence algebras",
      "singular cohomology groups",
      "finite dimensional incidence",
      "hochschild cohomology groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}