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arXiv · 2402.13621

Completely fixed point free isometry and cyclic orbifold of lattice vertex operator algebras

Hsian-Yang Chen·Ching Hung Lam
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Abstract

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.

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Hsian-Yang Chen, Ching Hung Lam. 2024-02-21. Completely fixed point free isometry and cyclic orbifold of lattice vertex operator algebras. https://arxiv.org/abs/2402.13621

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