Journal of Lie Theory

Turkowski has classified Lie algebras that have a non-trivial Levi decomposition of dimension up to and including nine. In this work the program is extended to give a partial classification of the corresponding Lie algebras in dimension ten. The key tool is the R-representation, which is the representation of the semi-simple factor by endomorphisms of the radical. The algebras studied here comprise 34 classes that have semi-simple factor so(3) and three exceptions for which semi-simple factor is of dimension six. Most of the algebras have an abelian nilradical, which is probably an artifact of the low dimensions involved. The many remaining cases where the semi-simple factor is sl(2, R) will be investigated in a different venue.