{
  "id": "2307.15952",
  "version": "v1",
  "published": "2023-07-29T10:47:06.000Z",
  "updated": "2023-07-29T10:47:06.000Z",
  "title": "The argument shift method in universal enveloping algebra $U\\mathfrak{gl}_d$",
  "authors": [
    "Y. Ikeda",
    "G. I. Sharygin"
  ],
  "comment": "13 pages, first draft",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "We prove the conjecture that allows one extend the argument shifting procedure from symmetric algebra $S\\mathfrak{gl}_d$ of the Lie algebra $\\mathfrak{gl}_d$ to the universal enveloping algebra $U\\mathfrak{gl}_d$. Namely, it turns out that the iterated quasi-derivations of the central elements in $U\\mathfrak{gl}_d$ commute with each other. Here quasi-derivation is a linear operator on $U\\mathfrak{gl}_d$, constructed by Gurevich, Pyatov and Saponov. This allows one better understand the structure of \\textit{argument shift algebras} (or \\textit{Mishchenko-Fomenko algebras}) in the universal enveloping algebra of $\\mathfrak{gl}_d$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-29T10:47:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B35",
      "17B63",
      "16S30",
      "81R12"
    ],
    "keywords": [
      "universal enveloping algebra",
      "argument shift method",
      "better understand",
      "linear operator",
      "argument shifting procedure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}