The main goal of this paper is to compute a minimal matrix representation for each non-isomorphicnilpotent Lie algebra of dimension less than 6. Indeed, for each of these algebras, we search thenatural number n ∈ N {1} such that the linear algebra n, formed by all the n × n complexstrictly upper-triangular matrices, contains a representation of this algebra. Besides, we show analgorithmic procedure which computes such a minimal representation by using the Lie algebrasn. In this way, a classification of such algebras according to the dimension of their minimalmatrix representations is obtained. In this way, we improve some results by Burde related to thevalue of the minimal dimension of the matrix representations for nilpotent Lie algebras.
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