  The main result of this paper is the conformal flatness of real-analytic
compact Lorentz manifolds of dimension at least $3$ admitting a conformal
essential (i.e. conformal, but not isometric) action of a Lie group locally
isomorphic to PSL(2,R). It is established by using a general result of M.
Gromov on local isometries of real-analytic $A$-rigid geometric structures. As
corollary, we deduce the same conclusion for conformal essential actions of
connected semi-simple Lie groups on real-analytic compact Lorentz manifolds.
This work is a contribution to the understanding of the Lorentzian version of a
question asked by A. Lichnerowicz.
