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Minimal Faithful Upper-Triangular Matrix Representations for Solvable Lie Algebras
A well-known result on Lie Theory states that every finite-dimensional
complex solvable Lie algebra can be represented as a matrix Lie algebra, with
upper-triangular square matrices as elements. However, this result does not
specify which is the minimal order of the matrices involved in such
representations. Hence, the main goal of this paper is to revisit and implement
a method to compute both that minimal order and a matrix representative for a
given solvable Lie algebra. As application of this procedure, we compute
representatives for each solvable Lie algebra with dimension less than .Comment: 19 pages, 6 table