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$ \mathbb{Z}_2$-orbifold construction associated with $ (-1)$-isometry and uniqueness of holomorphic vertex operator algebras of central charge 24


Authors: Kazuya Kawasetsu, Ching Hung Lam and Xingjun Lin
Journal: Proc. Amer. Math. Soc. 146 (2018), 1937-1950
MSC (2010): Primary 17B69
DOI: https://doi.org/10.1090/proc/13881
Published electronically: December 11, 2017
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Abstract: The vertex operator algebra structure of a strongly regular holomorphic vertex operator algebra $ V$ of central charge $ 24$ is proved to be uniquely determined by the Lie algebra structure of its weight one space $ V_1$ if $ V_1$ is a Lie algebra of the type $ A_{1,4}^{12}$, $ B_{2,2}^6$, $ B_{3,2}^4$, $ B_{4,2}^3$, $ B_{6,2}^2$, $ B_{12,2}$, $ D_{4,2}^2B_{2,1}^4$, $ D_{8,2}B_{4,1}^2$, $ A_{3,2}^4A_{1,1}^4$, $ D_{5,2}^2A_{3,1}^2$, $ D_{9,2}A_{7,1}$, $ C_{4,1}^4$, or $ D_{6,2}B_{3,1}^2C_{4,1}$.


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Additional Information

Kazuya Kawasetsu
Affiliation: Institute of Mathematics, Academia Sinica, Taipei 10617, Taiwan
Address at time of publication: School of Mathematics and Statistics, Faculty of Science, The University of Melbourne, Victoria 3052, Australia
Email: kazuya.kawasetsu@unimelb.edu.au

Ching Hung Lam
Affiliation: Institute of Mathematics, Academia Sinica, Taipei 10617, Taiwan
Email: chlam@math.sinica.edu.tw

Xingjun Lin
Affiliation: Institute of Mathematics, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan
Address at time of publication: Collaborative Innovation Centre of Mathematics, School of Mathematics and Statistics, Wuhan University, Luojiashan, Wuhan, Hubei 430072, People’s Republic of China
Email: linxingjun88@126.com

DOI: https://doi.org/10.1090/proc/13881
Keywords: Vertex operator algebra, orbifold construction, Niemeier lattices
Received by editor(s): January 3, 2017
Received by editor(s) in revised form: July 7, 2017
Published electronically: December 11, 2017
Additional Notes: The second author was partially supported by MoST grant 104-2115-M-001-004-MY3 of Taiwan
The third author is an “Overseas researchers under Postdoctoral Fellowship of Japan X1Society for the Promotion of Science” and is supported by JSPS Grant No. 16F16020.
Communicated by: Kailash C. Misra
Article copyright: © Copyright 2017 American Mathematical Society

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