Abstract
We obtain minimal dimension matrix representations for each of the Lie algebras of dimensions five, six, seven and eight obtained by Turkowski that have a non-trivial Levi decomposition. The key technique involves using the invariant subspaces associated to a particular representation of a semi-simple Lie algebra to help in the construction of the radical in the putative Levi decomposition.
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Ghanam, R., Lamichhane, M. & Thompson, G. Minimal representations of Lie algebras with non-trivial Levi decomposition. Arab. J. Math. 6, 281–296 (2017). https://doi.org/10.1007/s40065-017-0175-3
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DOI: https://doi.org/10.1007/s40065-017-0175-3