{
  "id": "2007.09918",
  "version": "v1",
  "published": "2020-07-20T07:59:11.000Z",
  "updated": "2020-07-20T07:59:11.000Z",
  "title": "Algebra of Borcherds products",
  "authors": [
    "Shouhei Ma"
  ],
  "categories": [
    "math.NT",
    "math.AG",
    "math.RA",
    "math.RT"
  ],
  "abstract": "Borcherds lift for an even lattice L of signature (p,q) is a lifting from weakly holomorphic modular forms of weight (p-q)/2 for the Weil representation of L. We introduce a product operation on the space of such modular forms, depending on the choice of a maximal isotropic sublattice of L, which makes this space a finitely generated filtered associative algebra, without unit element in general. This algebra structure is functorial with respect to embedding of lattices by the quasi-pullback map. We study the basic properties, prove for example that the algebra is commutative if and only if L is unimodular. When L is unimodular with p=2, the multiplicative group of Borcherds products of integral weight forms a subring.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-20T07:59:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F37",
      "16S99",
      "11F27",
      "11F55",
      "11F50"
    ],
    "keywords": [
      "borcherds products",
      "generated filtered associative algebra",
      "weakly holomorphic modular forms",
      "integral weight forms",
      "maximal isotropic sublattice"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}