Title: Minimal Representations of Lie Algebras With Non-Trivial Levi Decomposition,
Abstract: We obtain minimal dimension matrix representations for each of the Lie
algebras of dimension five, six, seven, and eight obtained by Turkowski that
have a non-trivial Levi decomposition. The Key technique involves using
subspace associated to a particular representation of semi-simple Lie algebra
to help in the construction of the radical in the putative Levi decomposition.