Invariant subalgebras of affine vertex algebras

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