{
  "id": "1902.06128",
  "version": "v1",
  "published": "2019-02-16T17:21:25.000Z",
  "updated": "2019-02-16T17:21:25.000Z",
  "title": "On Leibniz cohomology",
  "authors": [
    "Jörg Feldvoss",
    "Friedrich Wagemann"
  ],
  "categories": [
    "math.AT"
  ],
  "abstract": "In this paper we prove the Leibniz analogues of several vanishing theorems for the Chevalley-Eilenberg cohomology of Lie algebras. In particular , we obtain the second Whitehead lemma for Leibniz algebras. Our main tools are three spectral sequences. Two are Leibniz analogues of the Hochschild-Serre spectral sequence, one of which is an extension of the dual of a spectral sequence of Pirashvili for Leibniz homology from symmetric bi-modules to arbitrary bimodules, and the other one is due to Beaudouin. A third spectral sequence (also due to Pirashvili in homology) relates the Leibniz cohomology of a Lie algebra to its Chevalley-Eilenberg cohomology.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-16T17:21:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "leibniz cohomology",
      "lie algebra",
      "leibniz analogues",
      "chevalley-eilenberg cohomology",
      "third spectral sequence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}