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Application of a $ \mathbb{Z}_{3}$-orbifold construction to the lattice vertex operator algebras associated to Niemeier lattices


Authors: Daisuke Sagaki and Hiroki Shimakura
Journal: Trans. Amer. Math. Soc. 368 (2016), 1621-1646
MSC (2010): Primary 17B69
DOI: https://doi.org/10.1090/tran/6382
Published electronically: July 1, 2015
MathSciNet review: 3449220
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Abstract: By applying Miyamoto's $ \mathbb{Z}_{3}$-orbifold construction to the lattice vertex operator algebras associated to Niemeier lattices and their automorphisms of order $ 3$, we construct holomorphic vertex operator algebras of central charge $ 24$ whose Lie algebras of the weight one spaces are of types $ A_{2,3}^6$, $ E_{6,3}G_{2,1}^{3}$, and $ A_{5,3}D_{4,3}A_{1,1}^{3}$, which correspond to No.6, No.17, and No.32 on Schellekens' list, respectively.


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Additional Information

Daisuke Sagaki
Affiliation: Institute of Mathematics, University of Tsukuba, Tennodai 1-1-1, Tsukuba, Ibaraki 305-8571, Japan
Email: sagaki@math.tsukuba.ac.jp

Hiroki Shimakura
Affiliation: Graduate School of Information Sciences, Tohoku University, Aramaki aza Aoba 6-3-09, Aoba-ku, Sendai 980-8579, Japan
Email: shimakura@m.tohoku.ac.jp

DOI: https://doi.org/10.1090/tran/6382
Received by editor(s): May 18, 2013
Received by editor(s) in revised form: December 25, 2013
Published electronically: July 1, 2015
Additional Notes: The first author was partially supported by Grant-in-Aid for Young Scientists (B) No.23740003, Japan
The second author was partially supported by Grant-in-Aid for Scientific Research (C) No.23540013, Japan
Article copyright: © Copyright 2015 American Mathematical Society