{
  "id": "2312.14699",
  "version": "v1",
  "published": "2023-12-22T13:58:17.000Z",
  "updated": "2023-12-22T13:58:17.000Z",
  "title": "The Hochschild cohomology ring of monomial path algebras",
  "authors": [
    "Dalia Artenstein",
    "Janina C. Letz",
    "Amrei Oswald",
    "Andrea Solotar"
  ],
  "comment": "19 pages; comments are welcome",
  "categories": [
    "math.RT"
  ],
  "abstract": "We give an explicit description of a diagonal map on the Bardzell resolution for any monomial path algebra, and we use this diagonal map to describe the cup product on Hochschild cohomology. Then, we prove that the cup product is trivial in positive degrees for triangular monomial path algebras. Our proof uses the graded-commutativity of the cup product on Hochschild cohomology and does not rely on explicit computation of the Hochschild cohomology modules.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-22T13:58:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16E40",
      "18G10"
    ],
    "keywords": [
      "hochschild cohomology ring",
      "cup product",
      "diagonal map",
      "triangular monomial path algebras",
      "hochschild cohomology modules"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}