New examples of rank one solvable real rigid Lie algebras possessing a nonvanishing Chevalley cohomology

The class of rank one solvable Lie algebras possessing a maximal torus t with eigenvalue spectrum spec(t)=(1,4,5,…,n+2) is studied in the context of rigidity. It is shown that from the value n ≥ 18, three isomorphism classes of rigid Lie algebras exist, two of them being algebraically rigid, and the third being geometrically rigid with a two-dimensional cohomology space H2(g,g).