{
  "id": "1608.08934",
  "version": "v1",
  "published": "2016-08-31T16:39:52.000Z",
  "updated": "2016-08-31T16:39:52.000Z",
  "title": "Primitive ideals of $\\operatorname{U}(\\frak{sl}(\\infty))$",
  "authors": [
    "Ivan Penkov",
    "Alexey Petukhov"
  ],
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "We provide an explicit description of the primitive ideals of the enveloping algebra $\\operatorname{U}(\\frak{sl}(\\infty))$ of the infinite-dimensional finitary Lie algebra $\\frak{sl}(\\infty)$ over an uncountable algebraically closed field of characteristic 0. Our main new result is that any primitive ideal of $\\operatorname{U}(\\frak{sl}(\\infty))$ is integrable. A classification of integrable primitive ideals of $\\operatorname{U}(\\frak{sl}(\\infty))$ has been known previously, and relies on the pioneering work of A. Zhilinskii.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-31T16:39:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10",
      "17B35",
      "17B65"
    ],
    "keywords": [
      "primitive ideal",
      "infinite-dimensional finitary lie algebra",
      "explicit description",
      "enveloping algebra",
      "algebraically closed field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}