Faithful Representations of Minimal Dimension of 6-dimensional nilpotent Lie algebras

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The main goal of this paper is to compute μ() and μnil() for each nilpotent Lie algebra of dimension 6 over a field of characteristic zero. Here μ() and μnil() is the minimal dimension of a faithful representation of and the minimal dimension of a faithful nilrepresentation of, respectively. We also give a minimal faithful representation and nilrepresentation for each nilpotent Lie algebra of dimension ≤ 6.