{
  "id": "2103.02476",
  "version": "v1",
  "published": "2021-03-03T15:38:07.000Z",
  "updated": "2021-03-03T15:38:07.000Z",
  "title": "Tensor hierarchy extensions of hyperbolic Kac-Moody algebras",
  "authors": [
    "Martin Cederwall",
    "Jakob Palmkvist"
  ],
  "comment": "65 pages",
  "categories": [
    "math.RT",
    "hep-th"
  ],
  "abstract": "Tensor hierarchy algebras are infinite-dimensional generalisations of Cartan-type Lie superalgebras. They are not contragredient, exhibiting an asymmetry between positive and negative levels. These superalgebras have been a focus of attention due to the fundamental role they play for extended geometry. In the present paper, we examine tensor hierarchy algebras which are super-extensions of hyperbolic Kac-Moody algebras. They contain novel algebraic structures. Of particular interest is the extension of a hyperbolic algebra by its fundamental module, an extension that contains and generalises the extension of an affine Kac-Moody algebra by a Virasoro derivation $L_1$. A conjecture about the complete superalgebra is formulated, relating it to the corresponding Borcherds superalgebra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-03T15:38:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hyperbolic kac-moody algebras",
      "tensor hierarchy extensions",
      "tensor hierarchy algebras",
      "contain novel algebraic structures",
      "affine kac-moody algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 65,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}