Structure of perfect Lie algebras without center and outer derivations (Q1355493)

Let \(L\) be a Lie algebra over the real or complex numbers which is perfect and complete. The author calls such an algebra sympathetic. He constructs a 25-dimensional example and shows that any sympathetic algebra can be decomposed uniquely into the sum of irreducible sympathetic ideals. He shows the existence of a maximal sympathetic ideal called the sympathetic radical and studies its properties which include a version of the Levi-Malcev Theorem. Many related results are shown in this paper.