{
  "id": "0812.5013",
  "version": "v3",
  "published": "2008-12-30T21:37:25.000Z",
  "updated": "2009-11-30T05:43:00.000Z",
  "title": "Resultant as Determinant of Koszul Complex",
  "authors": [
    "A. Anokhina",
    "A. Morozov",
    "Sh. Shakirov"
  ],
  "comment": "32 pages, 12 figures",
  "journal": "Theor.Math.Phys. 160:3 (2009) 1203-1228",
  "categories": [
    "math-ph",
    "hep-th",
    "math.MP"
  ],
  "abstract": "A linear map between two vector spaces has a very important characteristic: a determinant. In modern theory two generalizations of linear maps are intensively used: to linear complexes (the nilpotent chains of linear maps) and to non-linear mappings. Accordingly, determinant of a linear map has two generalizations: to determinants of complexes and to resultants. These quantities are in fact related: resultant of a non-linear map is determinant of the corresponding Koszul complex. We give an elementary introduction into these notions and interrelations, which will definitely play a role in the future development of theoretical physics.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-11-30T05:43:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "determinant",
      "elementary introduction",
      "vector spaces",
      "corresponding koszul complex",
      "important characteristic"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s11232-009-0111-6",
      "journal": "Theoretical and Mathematical Physics",
      "year": 2009,
      "month": "Sep",
      "volume": 160,
      "number": 3,
      "pages": 1203
    },
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 806445,
      "adsabs": "2009TMP...160.1203A"
    }
  }
}