A remark on ${\mathbb{Z}}_p$-orbifold constructions of the Moonshine vertex operator algebra

Abstract

For $p=3,5,7,13$, we consider a ${\mathbb{Z}}_p$-orbifold construction of the Moonshine vertex operator algebra $V^{♮}$. We show that the vertex operator algebra obtained by the ${\mathbb{Z}}_p$-orbifold construction on the Leech lattice vertex operator algebra $V_{\Lambda }$ and a lift of a fixed-point-free isometry of order $p$ is isomorphic to the Moonshine vertex operator algebra $V^{♮}$. We also describe the relationship between those ${\mathbb{Z}}_p$-orbifold constructions and the ${\mathbb{Z}}_2$-orbifold construction in a uniform manner. In Appendix, we give a characterization of the Moonshine vertex operator algebra $V^{♮}$ by two mutually orthogonal Ising vectors.

13 pages, no figure. An error is fixed

Cited by in corpus (1)

• The Moonshine Anomaly