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• W3092880315 abstract "Given a finite dimensional Lie algebra g, let z(g) denote the center of g and let μ(g) be the minimal possible dimension for a faithful representation of g. In this paper we obtain μ(Lr,2), where Lr,k is the free k-step nilpotent Lie algebra of rank r. In particular we prove that μ(Lr,2)=⌈2r(r−1)⌉+2 for r≥4. It turns out that μ(Lr,2)∼μ(z(Lr,2))∼2dim⁡Lr,2 (as r→∞) and we present some evidence that this could be true for Lr,k for any k. This is considerably lower than the known bounds for μ(Lr,k), which are (for fixed k) polynomial in dim⁡Lr,k." @default.
• W3092880315 created "2020-10-22" @default.
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• W3092880315 date "2021-02-01" @default.
• W3092880315 modified "2023-10-16" @default.
• W3092880315 title "Minimal faithful representations of the free 2-step nilpotent Lie algebra of the rank r" @default.
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• W3092880315 doi "https://doi.org/10.1016/j.jalgebra.2020.10.001" @default.
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