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

Abstract 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 H 2 (g , g). [ABSTRACT FROM AUTHOR]