Fourvolutions and Automorphism Groups of Orbifold Lattice Vertex Operator Algebras

Let L be an even positive definite lattice with no roots, i.e., L(2) = {x is an element of L vertical bar (x vertical bar x) = 2} = phi . Let g is an element of O(L) be an isometry of order 4 such that g(2) = -1 on L. In this article, we determine the full automorphism group of the orbifold vertex b operator algebra V-L((g) over cap) . As our main result, we show that Aut (V-L((g) over cap)) is isomorphic to N-Aut(VL)(((g) over cap))/((g) over cap) unless L-similar or equal to root 2E(8) or BW16.