Fixed point subalgebras of lattice vertex operator algebras by an automorphism of order three

We study the fixed point subalgebra of a certain class of lattice vertex operator algebras by an automorphism of order 3, which is a lift of a fixed-point-free isometry of the underlying lattice. We classify the irreducible modules for the subalgebra. Moreover, the rationality and the $C_2$-cofiniteness of the subalgebra are established. Our result contains the case of the vertex operator algebra associated with the Leech lattice.Comment: 77 page

W-algebras related to parafermion algebras

We study a W-algebra of central charge 2(k-1)/(k+2) with k a positive integer greater than 1Comment: 37 page

Moonshine vertex operator algebra as L(12,0)⊗L(710,0)⊗L(45,0)⊗L(1,0)-modules

AbstractIn this article, we study the structure of the famous Moonshine vertex operator algebra V♮ as a module for a certain vertex operator subalgebra isomorphic to (L(12,0)⊗L(710,0)⊗L(45,0)⊗L(1,0))⊗8. As our main result, we obtain a complete decomposition of V♮ associated with this algebra. Our method is based on an embedding of the lattice (2A3)8 into the Leech lattice. Actually, we construct certain vertex operator algebras using some Z8 and Z2×Z2 codes. A decomposition of the Moonshine vertex operator algebra is obtained by a careful study of their representations