Abstract
For an even positive definite lattice L and its automorphism σ of order 3, we prove that a fixed point subVOA \(V_{L}^{\sigma}\) of a lattice VOA V L is C 2-cofinite. Using this result and the results in arXiv:0909.3665, we present ℤ3-orbifold constructions of holomorphic VOAs from lattice VOAs V Λ , where Λ are even unimodular positive definite lattices. One of them has the same character with the moonshine VOA V ♮ and another is a new VOA corresponding to No. 32 in Schellekens’ list (Theor. Mat. Fiz. 95(2), 348–360, 1993).
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Miyamoto, M. (2013). A ℤ3-Orbifold Theory of Lattice Vertex Operator Algebra and ℤ3-Orbifold Constructions. In: Iohara, K., Morier-Genoud, S., Rémy, B. (eds) Symmetries, Integrable Systems and Representations. Springer Proceedings in Mathematics & Statistics, vol 40. Springer, London. https://doi.org/10.1007/978-1-4471-4863-0_13
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DOI: https://doi.org/10.1007/978-1-4471-4863-0_13
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