{
  "id": "1901.07532",
  "version": "v1",
  "published": "2019-01-20T10:43:49.000Z",
  "updated": "2019-01-20T10:43:49.000Z",
  "title": "Cohomology of Restricted Filiform Lie Algebras $\\mathfrak{m}_2^λ(p)$",
  "authors": [
    "Tyler J. Evans",
    "Alice Fialowski"
  ],
  "comment": "17 pages. arXiv admin note: text overlap with arXiv:1801.08178",
  "categories": [
    "math.RT"
  ],
  "abstract": "Consider the $p$-dimensional filiform Lie algebra $\\mathfrak{m}_2(p)$ over a field $\\mathbb{F}$ of prime characteristic $p$ with nonzero Lie brackets $[e_1,e_i]=e_{i+1}$ for $1<i<p$ and $[e_2,e_i]=e_{i+2}$ for $2<i<p-1$. We show that there is a family $\\mathfrak{m}_2^{\\lambda}(p)$ of restricted Lie algebra structures parameterized by elements $\\lambda \\in \\mathbb{F}^p$. We explicitly describe bases for the the ordinary and restricted 1- and 2-cohomology spaces, and give formulas for the bracket and $[p]$-operations in the corresponding restricted one-dimensional central extensions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-20T10:43:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B50",
      "17B56"
    ],
    "keywords": [
      "restricted filiform lie algebras",
      "cohomology",
      "dimensional filiform lie algebra",
      "restricted lie algebra structures",
      "nonzero lie brackets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}