Abstract
In this paper, we compute minimal faithful unitriangular matrix representations of filiform Lie algebras. To do it, we use the nilpotent Lie algebra, \(\mathfrak{g}_n\), formed of n ×n strictly upper-triangular matrices. More concretely, we search the lowest natural number n such that the Lie algebra \(\mathfrak g_n\) contains a given filiform Lie algebra, also computing a representative of this algebra. All the computations in this paper have been done using MAPLE 9.5.
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