Schellekens' list and the very strange formula

@article{Ekeren2020SchellekensLA,
  title={Schellekens' list and the very strange formula},
  author={Jethro van Ekeren and Ching Hung Lam and Sven Karup M{\o}ller and Hiroki Shimakura},
  journal={arXiv: Quantum Algebra},
  year={2020}
}

Tables from this paper

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We prove a dimension formula for orbifold vertex operator algebras of central charge 24 by automorphisms of order $n$ such that $\Gamma_0(n)$ is a genus zero group. We then use this formula together
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Systematic Orbifold Constructions of Schellekens' Vertex Operator Algebras from Niemeier Lattices
We present a systematic, rigorous construction of all 70 strongly rational, holomorphic vertex operator algebras $V$ of central charge 24 with non-zero weight-one space $V_1$ as cyclic orbifold
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TLDR
An integral form is constructed for the universal enveloping algebra of any Kac-Moody algebras that can be used to define Kac's groups over finite fields, some new irreducible integrable representations, and a sort of affinization of anyKac-moody algebra.
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