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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Reverse orbifold construction and uniqueness of holomorphic vertex operator algebras
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by Ching Hung Lam and Hiroki Shimakura PDF
Trans. Amer. Math. Soc. 372 (2019), 7001-7024 Request permission

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
  • MR Author ID: 363106
  • Email: chlam@math.sinica.edu.tw
  • Hiroki Shimakura
  • Affiliation: Graduate School of Information Sciences, Tohoku University, Sendai 980-8579, Japan
  • MR Author ID: 688879
  • Email: shimakura@tohoku.ac.jp
  • 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”.
  • © Copyright 2019 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 372 (2019), 7001-7024
  • MSC (2010): Primary 17B69
  • DOI: https://doi.org/10.1090/tran/7887
  • MathSciNet review: 4024545