Coset construction of Z/3 orbifold vertex operator algebra

In this paper, we give a coset construction of the orbifold VOA , where τ is an order three automorphism of . The main idea is to use conjugations of several automorphisms of the lattice VOA VE6, which in some sense are analogous to Frenkel–Lepowsky–Meurman’s triality map. As a consequence, we construct explicitly many intertwining operators among modules of twisted type and obtain lower bounds for their fusion rules.