Some features of rank one real solvable cohomologically rigid lie algebras with a nilradical contracting onto the model filiform lie algebra Qn

The generic structure and some peculiarities of real rank one solvable Lie algebras possessing a maximal torus of derivations with the eigenvalue spectrum spec(t) = (1, k, k +1, ..., n + k-3, n +2k -3) for k [mayor o igual] 2 are analyzed, with special emphasis on the resulting Lie algebras for which the second Chevalley cohomology space vanishes. From the detailed inspection of the values k [menor o igual] 5, some series of cohomologically rigid algebras for arbitrary values of k are determined