  Given a finite-dimensional complex Lie algebra g equipped with a
nondegenerate, symmetric, invariant bilinear form B, let V_k(g,B) denote the
universal affine vertex algebra associated to g and B at level k. For any
reductive group G of automorphisms of V_k(g,B), we show that the invariant
subalgebra V_k(g,B)^G is strongly finitely generated for generic values of k.
This implies the existence of a new family of deformable W-algebras W(g,B,G)_k
which exist for all but finitely many values of k.
