Rank one lattice type vertex operator algebras and their automorphism groups -: II.: E-series

Let L be the A(1) root lattice and let G be a finite subgroup of Au(V), where V = V-L is the associated lattice VOA (in this case, Aut(V) congruent to PSL(2, C)). The fixed point sub-VOA, V-G, 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 congruent to Alt(4), Alt(5), or Sym(4). For such L and G, the above V-L(G) may be rational VOAs, (C) 1999 Academic Press.