Application of a ${\mathbb{Z}}_3$-orbifold construction to the lattice vertex operator algebras associated to Niemeier lattices

Abstract

By applying Miyamoto's ${\mathbb{Z}}_3$-orbifold construction to the lattice vertex operator algebras associated to Niemeier lattices and their automorphisms of order 3, we construct holomorphic vertex operator algebras of central charge 24 whose Lie algebras of the weight one spaces are of types $A_{2,3}^6$, $E_{6,3}{G}_{2,1}^3$, and $A_{5,3}{D}_{4,3}{A}_{1,1}^3$, which correspond to No.6, No.17, and No.32 on Schellekens' list, respectively.

References in corpus (2)

• Quadratic spaces and holomorphic framed vertex operator algebras of central charge 24
• Classification of holomorphic framed vertex operator algebras of central charge 24