Completely fixed point free isometry and cyclic orbifold of lattice vertex operator algebras
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910338949054464 |
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| author | Chen, Hsian-Yang Lam, Ching Hung |
| author_facet | Chen, Hsian-Yang Lam, Ching Hung |
| contents | We continue our study of cyclic orbifolds of lattice vertex operator algebras and their full automorphism groups. We consider some special isometry $g\in O(L)$ such that $g^i$ is fixed point free on $L$ for any $1\leq i\leq |g|-1$. We show that when $L_2=\emptyset$ and $g^i$ is fixed point free on $L$ for any $1\leq i\leq |g|-1$, $V_L^{\hat{g}}$ has extra automorphisms implies either (1) the order of $g$ is a prime or (2) $L$ is isometric to the Leech lattice or some coinvariant sublattices of the Leech lattice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_13621 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Completely fixed point free isometry and cyclic orbifold of lattice vertex operator algebras Chen, Hsian-Yang Lam, Ching Hung Quantum Algebra 17B69 We continue our study of cyclic orbifolds of lattice vertex operator algebras and their full automorphism groups. We consider some special isometry $g\in O(L)$ such that $g^i$ is fixed point free on $L$ for any $1\leq i\leq |g|-1$. We show that when $L_2=\emptyset$ and $g^i$ is fixed point free on $L$ for any $1\leq i\leq |g|-1$, $V_L^{\hat{g}}$ has extra automorphisms implies either (1) the order of $g$ is a prime or (2) $L$ is isometric to the Leech lattice or some coinvariant sublattices of the Leech lattice. |
| title | Completely fixed point free isometry and cyclic orbifold of lattice vertex operator algebras |
| topic | Quantum Algebra 17B69 |
| url | https://arxiv.org/abs/2402.13621 |