Cohomological criterion for extending derivations (Q1110642)

Let \(0\to H\to L\to M\to 0\) be an exact sequence of Lie algebras. The authors give a cohomological criterion for extending a pair (\(\sigma,\tau)\in Der(M)\times Der(H)\) to a derivation of L and use it to derive a criterion for completeness for solvable finite-dimensional Lie algebras. Then as a corollary they give a construction of a complete solvable Lie algebra beginning with any solvable Lie algebra with trivial center.