{
  "id": "1801.08178",
  "version": "v1",
  "published": "2018-01-24T20:41:45.000Z",
  "updated": "2018-01-24T20:41:45.000Z",
  "title": "Restricted One-dimensional Central Extensions of the Restricted Filiform Lie Algebras ${\\frak m}_0^λ(p)$",
  "authors": [
    "Tyler J. Evans",
    "Alice Fialowski"
  ],
  "comment": "17 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "We show, for a field ${\\mathbb F}$ of prime characteristic $p>0$, that the truncated filiform Lie algebra ${\\frak m}_0(p)$ admits a family ${\\frak m}_0^\\lambda(p)$ of restricted Lie algebra structures parameterized by elements $\\lambda\\in {\\mathbb F}^p$. We compute the ordinary cohomology groups $H^q({\\frak m}_0^\\lambda(p))$ and restricted cohomology groups $H^q_*({\\frak m}_0^\\lambda(p))$ for $q=1, 2$, and we give explicit descriptions of bases for these cohomology spaces. We apply our results to restricted one-dimensional central Extensions of the algebras ${\\frak m}_0^\\lambda(p)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-24T20:41:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B56",
      "15B50"
    ],
    "keywords": [
      "restricted one-dimensional central extensions",
      "restricted filiform lie algebras",
      "truncated filiform lie algebra",
      "restricted lie algebra structures",
      "ordinary cohomology groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}