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

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- by Kazuya Kawasetsu, Ching Hung Lam and Xingjun Lin PDF
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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 $D_{6,2}B_{3,1}^2C_{4,1}$.## References

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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
- MR Author ID: 1049830
- Email: kazuya.kawasetsu@unimelb.edu.au
**Ching Hung Lam**- Affiliation: Institute of Mathematics, Academia Sinica, Taipei 10617, Taiwan
- MR Author ID: 363106
- 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
- MR Author ID: 975866
- Email: linxingjun88@126.com
- 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
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**146**(2018), 1937-1950 - MSC (2010): Primary 17B69
- DOI: https://doi.org/10.1090/proc/13881
- MathSciNet review: 3767347