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.
Kenichiro TANABE. Hiromichi YAMADA. "Fixed point subalgebras of lattice vertex operator algebras by an automorphism of order three." J. Math. Soc. Japan 65 (4) 1169 - 1242, October, 2013. https://doi.org/10.2969/jmsj/06541169