{
  "id": "2405.08325",
  "version": "v1",
  "published": "2024-05-14T05:48:23.000Z",
  "updated": "2024-05-14T05:48:23.000Z",
  "title": "Centers of Universal Enveloping Algebras",
  "authors": [
    "Yaping Yang",
    "Daihao Zeng"
  ],
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "The universal enveloping algebra $U(\\mathfrak{g} )$ of a current (super)algebra or loop (super)algebra $\\mathfrak{g} $ is considered over an algebraically closed field $\\mathbb{K} $ with characteristic $p\\ge 0$. This paper focuses on the structure of the center $Z(\\mathfrak{g} )$ of $U(\\mathfrak{g} )$. In the case of zero characteristic, $Z(\\mathfrak{g} )$ is generated by the centers of $\\mathfrak{g} $. In the case of prime characteristic, $Z(\\mathfrak{g} )$ is generated by the centers of $\\mathfrak{g} $ and the $p$-centers of $U(\\mathfrak{g} )$. We also study the structure of $Z(\\mathfrak{g} )$ in the semisimple Lie (super)algebra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-14T05:48:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "universal enveloping algebra",
      "paper focuses",
      "zero characteristic",
      "prime characteristic",
      "semisimple lie"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}