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Minimal Representations of Lie Algebras With Non-Trivial Levi Decomposition (1703.05453v2)
Published 16 Mar 2017 in math.RT
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.