Extra automorphisms of cyclic orbifolds of lattice vertex operator algebras

Abstract

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 $p$.

37 pages

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• Automorphism groups of cyclic orbifold vertex operator algebras associated with the Leech lattice and some non-prime isometries