Contributions to real exponential Lie groups
Necessary and sufficient conditions are given for the exponentiality of real Lie groups of mixed type, i.e. groups which are neither solvable nor semisimple. Necessary conditions are proved in Section 2 for connected real Lie groups to be exponential (Theorems 2 and 3), and sufficient conditions are given for real algebraic groups which are semidirect products of compact connected Lie groups acting on simply connected solvable Lie groups which are exponential themselves (Theorem 4), and also for connected Mal'cev splittable Lie groups satisfying some properties with respect to their Lie algebras (Theorem 5). All conditions deal with the centralizers of ad-nilpotent elements of the corresponding Lie algebras. A ``universal'' counterexample shows at last that all these criteria are not necessary \textit{and} sufficient.
scientific article; zbMATH DE number 1466225