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.