{
  "id": "1003.2332",
  "version": "v1",
  "published": "2010-03-11T13:32:43.000Z",
  "updated": "2010-03-11T13:32:43.000Z",
  "title": "Torsion theories induced from commutative subalgebras",
  "authors": [
    "Vyacheslav Futorny",
    "Serge Ovsienko",
    "Manuel Saorin"
  ],
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "We begin a study of torsion theories for representations of an important class of associative algebras over a field which includes all finite W-algebras of type A, in particular the universal enveloping algebra of gl(n) (or sl(n)) for all n. If U is such and algebra which contains a finitely generated commutative subalgebra A, then we show that any A-torsion theory defined by the coheight of prime ideals is liftable to U. Moreover, for any simple U-module M, all associated prime ideals of M in Spec A have the same coheight. Hence,thecoheight of the associated prime ideals of A is an invariant of a given simple U-module. This implies a stratification of the category of $U$-modules controlled by the coheight of associated prime ideals of A. Our approach can be viewed as a generalization of the classical paper by R.Block, it allows in particular to study representations of gl(n) beyond the classical category of weight or generalized weight modules.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-03-11T13:32:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16D60",
      "16D90",
      "16D70",
      "17B65"
    ],
    "keywords": [
      "torsion theories",
      "commutative subalgebra",
      "associated prime ideals",
      "simple u-module",
      "generalized weight modules"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1003.2332F"
    }
  }
}