Automorphism groups of the holomorphic vertex operator algebras associated with Niemeier lattices and the $-1$-isometries

Abstract

In this article, we determine the automorphism groups of 14 holomorphic vertex operator algebras of central charge 24 obtained by applying the $\mathbb{Z}_2$-orbifold construction to the Niemeier lattice vertex operator algebras and lifts of the $-1$-isometries.