Extra automorphisms of cyclic orbifolds of lattice vertex operator algebras
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866912041501982720 |
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| author | Lam, Ching Hung Shimakura, Hiroki |
| author_facet | Lam, Ching Hung Shimakura, Hiroki |
| contents | In this article, we study the automorphism group of the cyclic orbifold of a vertex operator algebra associated with a rootless even lattice for a lift of a fixed-point free isometry of odd prime order $p$. We prove that such a cyclic orbifold contains extra automorphisms, not induced from automorphisms of the lattice vertex operator algebra, if and only if the rootless even lattice can be constructed by Construction B from a code over $\mathbb{Z}_p$ or is isometric to the coinvariant lattice of the Leech lattice associated with a certain isometry of order $p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_08085 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Extra automorphisms of cyclic orbifolds of lattice vertex operator algebras Lam, Ching Hung Shimakura, Hiroki Quantum Algebra Combinatorics Group Theory 17B69 In this article, we study the automorphism group of the cyclic orbifold of a vertex operator algebra associated with a rootless even lattice for a lift of a fixed-point free isometry of odd prime order $p$. We prove that such a cyclic orbifold contains extra automorphisms, not induced from automorphisms of the lattice vertex operator algebra, if and only if the rootless even lattice can be constructed by Construction B from a code over $\mathbb{Z}_p$ or is isometric to the coinvariant lattice of the Leech lattice associated with a certain isometry of order $p$. |
| title | Extra automorphisms of cyclic orbifolds of lattice vertex operator algebras |
| topic | Quantum Algebra Combinatorics Group Theory 17B69 |
| url | https://arxiv.org/abs/2103.08085 |