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

Abstract

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.

77 pages

References in corpus (1)

• On intertwining operators and finite automorphism groups of vertex operator algebras

Cited by in corpus (2)

• The irreducible weak modules for the fixed point subalgebra of the vertex algebra associated to a non-degenerate even lattice by an automorphism of order $2$ (Part $1$)
• A generalization of intertwining operators for vertex operator algebras