{
  "id": "2106.16178",
  "version": "v1",
  "published": "2021-06-30T16:13:30.000Z",
  "updated": "2021-06-30T16:13:30.000Z",
  "title": "Three Families of Lie Algebras of Exponential Growth from Vertex Operator Algebras",
  "authors": [
    "Gabriel B. Legros"
  ],
  "comment": "PhD dissertation, 2021, 152 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "We study three families of infinite-dimensional Lie algebras defined from Vertex Operator Algebras and their properties. For $N=0$ VOAs, we review the construction of the Fock space $V_L$ from an even lattice $L$ and provide an algebraic description of the Lie algebra $g_{II_{25,1}}$ from the perspective of $24$ different Niemeier lattices $N$ via the decomposition $II_{25,1} = N \\oplus II_{1,1}$ using the no-ghost theorem. For $N=1$ SVOAs we review the construction of the Fock space $V_{NS}$ and provide an explicit basis for the spectrum-generating algebra of the Lie algebra $g_{NS}$. For $N=2$ SVOAs, we describe the structure of $g^{(2)}_{NS}$ explicitly as a $\\mathbb{Q}$-graded Lie algebra and we lift a left and right $SL(2,\\mathbb{Z})$ action on $II_{2,2}$ to $g^{(2)}_{NS}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-30T16:13:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "vertex operator algebras",
      "exponential growth",
      "fock space",
      "infinite-dimensional lie algebras",
      "graded lie algebra"
    ],
    "tags": [
      "dissertation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 152,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}