Application of a ℤ₃-orbifold construction to the lattice vertex operator algebras associated to Niemeier lattices

Sagaki, Daisuke; Shimakura, Hiroki

doi:10.1090/tran/6382

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.

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