{
  "id": "1302.3992",
  "version": "v1",
  "published": "2013-02-16T19:33:20.000Z",
  "updated": "2013-02-16T19:33:20.000Z",
  "title": "An algebro-geometric construction of lower central series of associative algebras",
  "authors": [
    "David Jordan",
    "Hendrik Orem"
  ],
  "categories": [
    "math.AG",
    "math.RA"
  ],
  "abstract": "The lower central series invariants M_k of an associative algebra A are the two-sided ideals generated by k-fold iterated commutators; the M_k provide a filtration of A. We study the relationship between the geometry of X = Spec A_ab and the associated graded components N_k of this filtration. We show that the N_k form coherent sheaves on a certain nilpotent thickening of X, and that Zariski localization on X coincides with noncommutative localization of A. Under certain freeness assumptions on A, we give an alternative construction of N_k purely in terms of the geometry of X (and in particular, independent of A). Applying a construction of Kapranov, we exhibit the N_k as natural vector bundles on the category of smooth schemes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-02-16T19:33:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14A22"
    ],
    "keywords": [
      "associative algebra",
      "algebro-geometric construction",
      "lower central series invariants",
      "form coherent sheaves",
      "natural vector bundles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.3992J"
    }
  }
}