  In this paper we continue our work on Schwartz functions and generalized
Schwartz functions on Nash (i.e. smooth semi-algebraic) manifolds. Our first
goal is to prove analogs of de-Rham theorem for de-Rham complexes with
coefficients in Schwartz functions and generalized Schwartz functions. Using
that we compute cohomologies of the Lie algebra of an algebraic group G with
coefficients in the space of generalized Schwartz sections of G-equivariant
bundle over a G-transitive variety M. We do it under some assumptions on
topological properties of G and M. This computation for the classical case is
known as Shapiro lemma.
