Real rigid solvable Lie algebras are not necessarily completely solvable (Q855556)

The authors show that a real rigid solvable Lie algebra is not necessarily completely solvable. They construct an example \(\mathfrak n\oplus \mathfrak t\) of minimal dimension where the exterior torus \(\mathfrak t\) is not formed by ad-semisimple derivations on \(\mathbb R\). They also study real forms of nilradicals of rigid solvable Lie algebras of dimension \(n\leq 7\) and give a classification of rigid solvable Lie algebras of dimension 8 over \(\mathbb R\) .