{
  "id": "2006.12942",
  "version": "v1",
  "published": "2020-06-23T12:37:48.000Z",
  "updated": "2020-06-23T12:37:48.000Z",
  "title": "Projective dimension and commuting variety of a reductive Lie algebra",
  "authors": [
    "Jean-Yves Charbonnel"
  ],
  "categories": [
    "math.AG",
    "math.RT"
  ],
  "abstract": "The commuting variety of a reductive Lie algebra g is the underlying variety of a well defined subscheme of g x g. In this note, it is proved that this scheme is normal and Cohen-Macaulay. In particular, its ideal of definition is a prime ideal. As a matter of fact, this theorem results from a so called Property (P) for a simple Lie algebra. This property says that some cohomology complexes are exact.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-23T12:37:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "reductive lie algebra",
      "commuting variety",
      "projective dimension",
      "simple lie algebra",
      "property says"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}