We give a complete description of semi-symmetric algebraic curvature tensors on a four-dimensional Lorentzian vector space and we use this description to determine all four-dimensional homogeneous semi-symmetric Lorentzian manifolds.Theorem 1.1. Let M be a four-dimensional homogeneous semi-symmetric Lorentzian manifold. Then its Ricci operator is either diagonolizable or satisfies Ric 0 and Ric 2 = 0 and one of the following situation occurs:
If Ric has a non null eigenvalue then M is locally isometric to a Lie group with a left invariant metric or M isRicci parallel and in this case one of the following situations occurs: