# Construction and classification of holomorphic vertex operator algebras

@article{vanEkeren2020ConstructionAC,
title={Construction and classification of holomorphic vertex operator algebras},
author={Jethro van Ekeren and Sven M{\"o}ller and Nils R. Scheithauer},
journal={Journal f{\"u}r die reine und angewandte Mathematik (Crelles Journal)},
year={2020},
volume={2020},
pages={61 - 99}
}
• Published 29 July 2015
• Mathematics
• Journal für die reine und angewandte Mathematik (Crelles Journal)
Abstract We develop an orbifold theory for finite, cyclic groups acting on holomorphic vertex operator algebras. Then we show that Schellekens’ classification of V1{V_{1}}-structures of meromorphic conformal field theories of central charge 24 is a theorem on vertex operator algebras. Finally, we use these results to construct some new holomorphic vertex operator algebras of central charge 24 as lattice orbifolds.
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We associate with a generalised deep hole of the Leech lattice vertex operator algebra a generalised hole diagram. We show that this Dynkin diagram determines the generalised deep hole up to
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We discuss some basic problems and conjectures in a program to construct general orbifold conformal field theories using the representation theory of vertex operator algebras. We first review a
Title ORBIFOLD VERTEX OPERATOR ALGEBRAS AND THE POSITIVITY CONDITION (Research on algebraic combinatorics and representation theory of finite groups and vertex operator algebras)
In this note we show that the irreducible twisted modules of a holomorphic, C_{2}‐cofinite vertex operator algebra V have L_{0}‐weights at least as large as the smaılest L_{0}‐weight of V . Hence, if
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We introduce the notion of a genus and its mass for vertex algebras. For lattice vertex algebras, their genera are the same as those of lattices, which plays an important role in the classification
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• 2018
Abstract In this paper, we study orbifold constructions associated with the Leech lattice vertex operator algebra. As an application, we prove that the structure of a strongly regular holomorphic

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