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

We continue our study of cyclic orbifolds of lattice vertex operator algebras and their full automorphism groups. We consider some special isometry g is an element of O(L) such that gi is fixed point free on L for any 1 <= i <= |g| - 1. We show that when L(2) = & empty; and gi is fixed point free on L for any 1 <= i <= |g| - 1, V-L(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. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and datamining, AI training, and similar technologies.