Algèbres de Lie \({\mathfrak g}\) satisfaisant \([{\mathfrak g,g}]={\mathfrak g}\), Der\({\mathfrak g} = \)ad\({\mathfrak g}\). (Lie algebras \({\mathfrak g}\) satisfying \([{\mathfrak g,g}]={\mathfrak g}\), Der\({\mathfrak g} = \)ad\({\mathfrak g}\)). (French) Zbl 0647.17006

The author exhibits a class of non-semisimple Lie algebras \({\mathfrak g}\) satisfying [\({\mathfrak g,g}]={\mathfrak g}\) and Der \({\mathfrak g}=ad {\mathfrak g}\). In his examples \({\mathfrak g}\) is the sum of a semisimple algebra \({\mathfrak s}\) and a nilpotent algebra \({\mathfrak n}\) which is a sum of four \({\mathfrak s}\)- modules with Lie product satisfying certain conditions.
Reviewer: G.Brown


17B05 Structure theory for Lie algebras and superalgebras
17B40 Automorphisms, derivations, other operators for Lie algebras and super algebras