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On orbifold constructions associated with the Leech lattice vertex operator algebra

Published online by Cambridge University Press:  05 September 2018

CHING HUNG LAM  and
HIROKI SHIMAKURA
CHING HUNG LAM
Affiliation:
Institute of Mathematics, Academia Sinica and National Center for Theoretical Sciences of Taiwan, Taipei 10617, Taiwan. e-mail: chlam@math.sinica.edu.tw
HIROKI SHIMAKURA
Affiliation:
Graduate School of Information Sciences, Tohoku University, Sendai 980-8579, Japan. e-mail: shimakura@tohoku.ac.jp
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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 vertex operator algebra of central charge 24 is uniquely determined by its weight one Lie algebra if the Lie algebra has the type A3,43A1,2, A4,52, D4,12A2,6, A6,7, A7,4A1,13, D5,8A1,2 or D6,5A1,12 by using the reverse orbifold construction. Our result also provides alternative constructions of these vertex operator algebras (except for the case A6,7) from the Leech lattice vertex operator algebra.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 168 , Issue 2 , March 2020 , pp. 261 - 285
Copyright
Copyright © Cambridge Philosophical Society 2018 

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Footnotes

†

Partially supported by MoST grant 104-2115-M-001-004-MY3 of Taiwan.

‡

Partially supported by JSPS KAKENHI Grant Numbers JP26800001 and JP17K05154.

§

Both authors were partially supported by JSPS Program for Advancing Strategic International Networks to Accelerate the Circulation of Talented Researchers “Development of Concentrated Mathematical Center Linking to Wisdom of the Next Generation”.

References

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