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

摘要

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