Hochschild-Serre Statement for the total cohomology

Let M be a complex manifold and F a Om-module with a g-holomorphic action where g is a complex Lie algebra (cf. [3]). We denote by H(g, F) the "total cohomology" as defined in [1] [2]. Then we prove that, for any ideal a c g,the module H* (a, F) viewed as a g/a-module, we have a spectral sequence which converges to H(g, F)