Moskowitz, Martin; Wüstner, Michael Exponentiality of certain real solvable Lie groups. (English) Zbl 0913.22007 Can. Math. Bull. 41, No. 3, 368-373 (1998). A connected Lie group \(G\) is called exponential if its exponential function \(\exp : {\mathbf g} \to G\) is surjective. In general it is quite hard to prove or disprove that a given Lie group \(G\) is exponential. In [Math. Nachr. 192, 255-267 (1998; Zbl 0904.22004)] the second author describes various characterizations of solvable exponential Lie groups. One condition characterizing exponential solvable Lie groups is that the centralizers of all \(ad\)-nilpotent elements in \({\mathbf g}\) in a Cartan subgroup \(H \subseteq G\) are connected. The first main result of the paper under review simplifies this criterion for groups of the type \(G = N \mathrel\times T\), where \(N\) is nilpotent and \(T\) a torus. It is shown that \(G\) is exponential if and only if the centralizer in \(T\) of each element in the Lie algebra of \(N\) is connected. The second main result is a more technical statement dealing with semidirect products \(N \mathrel\times T\), where \(N\) is solvable. Reviewer: K.-H.Neeb (Darmstadt) Cited in 1 ReviewCited in 4 Documents MSC: 22E25 Nilpotent and solvable Lie groups 22E15 General properties and structure of real Lie groups Keywords:exponential function; exponential group; Lie group; solvable Lie group Citations:Zbl 0904.22004 PDFBibTeX XMLCite \textit{M. Moskowitz} and \textit{M. Wüstner}, Can. Math. Bull. 41, No. 3, 368--373 (1998; Zbl 0913.22007) Full Text: DOI