A holomorphic foliation F on a compact complex manifold M is
said to be an L-foliation if there exists an action of a complex
Lie group G such that the generic leaf of F coincides with the
generic orbit of G. We study L-foliations of codimension one, in
particular in projective space, in the spirit of classical invariant theory,
but here the invariants are sometimes transcendantal ones. We give a bestiary
of examples and general properties. Some classification results are obtained in
low dimensions