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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Reverse orbifold construction and uniqueness of holomorphic vertex operator algebras


Authors: Ching Hung Lam and Hiroki Shimakura
Journal: Trans. Amer. Math. Soc. 372 (2019), 7001-7024
MSC (2010): Primary 17B69
DOI: https://doi.org/10.1090/tran/7887
Published electronically: June 28, 2019
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Abstract: In this article, we develop a general technique for proving the uniqueness of holomorphic vertex operator algebras based on the orbifold construction and its ``reverse'' process. 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 $ 1$ Lie algebra if the Lie algebra has the type $ E_{6,3}G_{2,1}^3$, $ A_{2,3}^6$, or $ A_{5,3}D_{4,3}A_{1,1}^3$.


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Additional Information

Ching Hung Lam
Affiliation: Institute of Mathematics, Academia Sinica, Taipei 10617, Taiwan and National Center for Theoretical Sciences of Taiwan, Taipei, Taiwan
Email: chlam@math.sinica.edu.tw

Hiroki Shimakura
Affiliation: Graduate School of Information Sciences, Tohoku University, Sendai 980-8579, Japan
Email: shimakura@tohoku.ac.jp

DOI: https://doi.org/10.1090/tran/7887
Received by editor(s): March 5, 2017
Received by editor(s) in revised form: November 19, 2018
Published electronically: June 28, 2019
Additional Notes: The first author was partially supported by MoST Grant Number 104-2115-M-001-004-MY3 of Taiwan
The second author was partially supported by JSPS KAKENHI Grant Numbers 26800001 and 17K05154
The authors were partially supported by the 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”.
Article copyright: © Copyright 2019 American Mathematical Society