Cohomology of solvable lie algebras and solvmanifolds

The cohomology H _{\mathfrakg\mathfrak{g} ) of the tangent Lie algebra \mathfrakg\mathfrak{g} of the group G with coefficients in the one-dimensional representation \mathfrakg\mathfrak{g} \mathbbK\mathbb{K} defined by (W)\tilde] \mathfrakg \tilde \Omega _\mathfrak{g} of H ¹(G/ \mathfrakg\mathfrak{g} .}