The automorphism group of the vertex operator algebra VL+​ is studied by
using its action on isomorphism classes of irreducible VL+​-modules. In
particular, the shape of the automorphism group of VL+​ is determined when
L is isomorphic to an even unimodular lattice without roots, 2​R for an
irreducible root lattice R of type ADE and the Barnes-Wall lattice of rank
16.Comment: 29 page