The fixed point subalgebra of a lattice vertex operator algebra by an   automorphism of order three
  We study the subalgebra of the lattice vertex operator algebra $V_{\sqrt{2}A_2}$ consisting of the fixed points of an automorphism which is induced from an order 3 isometry of the root lattice $A_2$. We classify the simple modules for the subalgebra. The rationality and the $C_2$-cofiniteness are also established. 
Kenichiro Tanabe, Hiromichi Yamada