Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Schellekens' List and the Very Strange Formula   In 1993 Schellekens proved that the weight-one space $V_1$ of a strongly
rational, holomorphic vertex operator algebra $V$ of central charge 24 must be
one of 71 Lie algebras. During the following three decades, in a combined
effort by many authors, it was proved that each of these Lie algebras is
realised by such a vertex operator algebra and that, except for $V_1=\{0\}$,
this vertex operator algebra is uniquely determined by $V_1$.
  In this paper we give a fundamentally different, simpler proof of
Schellekens' list of 71 Lie algebras. Using the dimension formula in
arXiv:1910.04947 and Kac's "very strange formula" we show that every strongly
rational, holomorphic vertex operator algebra $V$ of central charge 24 with
$V_1\neq\{0\}$ can be obtained by an orbifold construction from the Leech
lattice vertex operator algebra $V_\Lambda$. This suffices to restrict the
possible Lie algebras that can occur as weight-one space of $V$ to the 71 of
Schellekens.
  Moreover, the fact that each strongly rational, holomorphic vertex operator
algebra $V$ of central charge 24 comes from the Leech lattice $\Lambda$ can be
used to classify these vertex operator algebras by studying properties of the
Leech lattice. We demonstrate this for 43 of the 70 non-zero Lie algebras on
Schellekens' list, omitting those cases that are too computationally expensive.

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The categories of this paper are: solv-int
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The categories of this paper are: hep-ph
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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin