The automorphism group of the vertex operator algebra for an even lattice L without roots

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