{
  "id": "1711.05080",
  "version": "v2",
  "published": "2017-11-14T12:31:48.000Z",
  "updated": "2017-12-09T09:29:59.000Z",
  "title": "Homology of the Lie algebra $\\mathfrak{gl}(\\infty,R)$",
  "authors": [
    "A. Fialowski",
    "K. Iohara"
  ],
  "comment": "14 pages, minor corrections, Section 6.6 added",
  "categories": [
    "math.RT",
    "math-ph",
    "math.KT",
    "math.MP"
  ],
  "abstract": "In this note we compute the homology of the Lie algebra $\\mathfrak{gl}(\\infty,R)$ where $R$ is an associative unital $k$-algebra which is used in higher dimensional soliton theory. When $k$ is a field of characteristic $0$, our result justifies an old result of Feigin and Tsygan appeared in 1983. The special case when $R=k$ is the complex number field $\\mathbb{C}$ appeared first in soliton theory.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2017-12-09T09:29:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lie algebra",
      "higher dimensional soliton theory",
      "complex number field",
      "result justifies",
      "old result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}