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

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- by Daisuke Sagaki and Hiroki Shimakura PDF
- Trans. Amer. Math. Soc.
**368**(2016), 1621-1646 Request permission

## 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.## References

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## Additional Information

**Daisuke Sagaki**- Affiliation: Institute of Mathematics, University of Tsukuba, Tennodai 1-1-1, Tsukuba, Ibaraki 305-8571, Japan
- MR Author ID: 680572
- 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
- MR Author ID: 688879
- Email: shimakura@m.tohoku.ac.jp
- 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 - © Copyright 2015 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**368**(2016), 1621-1646 - MSC (2010): Primary 17B69
- DOI: https://doi.org/10.1090/tran/6382
- MathSciNet review: 3449220