Decomposition of the Moonshine Vertex Operator Algebra as Virasoro Modules

AbstractIn this article, we obtain a decomposition of the Moonshine vertex operator algebra V♮ associated with the algebra (L(1/2,0)⊗L(7/10,0)⊗L(4/5,0))⊗12. Our method is based on a coset decomposition of the Leech lattice Λ associated with 2A212 using some codes. In fact, we construct a code vertex operator algebra MkC⊗MtD with a ternary code D and a Z2×Z2 code C and use it to obtain a decomposition of V♮