Representations of a fixed-point subalgebra of a class of lattice vertex operator algebras by an automorphism of order three

This is a summary of our recent work. We study a 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. The classification of the irreducible modules, together with 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.