Rank One Lattice Type Vertex Operator Algebras and Their Automorphism Groups II. E-Series

Let L be the A1 root lattice and let G be a finite subgroup of Au(V), where V = VL is the associated lattice VOA (in this case, Aut(V) PSL(2, )). The fixed point sub-VOA, VG, was studied previously by the authors, who found a set of generators and determined the automorphism group when G is cyclic (from the “A-series”) or dihedral (from the “D-series”). In the present article, we obtain analogous results for the remaining possibilities for G, that it belong to the “E-series”: G Alt4, Alt5, or Sym4. For such L and G, the above VGL may be rational VOAs.