Projectable Lie algebras of vector fields in 3D

Starting with Lie's classification of finite-dimensional transitive Lie algebras of vector fields on C2 we construct transitive Lie algebras of vector fields on the bundle C2×C by lifting the Lie algebras from the base. There are essentially three types of transitive lifts and we compute all of them for the Lie algebras from Lie's classification. The simplest type of lift is encoded by Lie algebra cohomology.