On wild and tame finite-dimensional Lie algebras (Q482571)

The purpose of this paper is to determine the finite-dimensional Lie algebras over an algebraically closed field of zero characteristic and such that the classification problem of finite dimensional modules is tame. While it is known that semisimple algebras are tame, solvable Lie algebras are wild, hence the classification reduces essentially to analyze semidirect sums. The main result states that, besides the semisimple case, the only tame algebras are the semidirect sums of semisimple algebras with the one-dimensional abelian Lie algebra.