Semidirect sums of Lie algebras

This paper examines the problem of classifying finite-dimensional Lie algebras over the field C with a given radical (mathfrak{r}) and also the problem of classifying algebraic Lie algebras with a given nilpotent radical (mathfrak{r}) . A detailed study is made of the case when (mathfrak{r}) is the nilpotent radical of a parabolic subalgebra of a semisimple Lie algebra.