On Z(p)-orbifold constructions of the Moonshine vertex operator algebra

摘要

For p = 3, 5, 7, 13, we consider a Z(p)-orbifold construction of the Moonshine vertex operator algebra V-(sic). We show that the vertex operator algebra obtained by the 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-(sic). We also describe the relationship between those Z(p)-orbifold constructions and the Z(2)-orbifold construction in a uniform manner. In Appendix, we give a characterization of the Moonshine vertex operator algebra V-(sic) by the existence of an orthogonal pair of Ising vectors.