Computing faithful representations for nilpotent Lie algebras

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dc.creatorBurde, Dietrich
dc.creatorEick, Bettina
dc.creatorde Graaf, Willem
dc.date2008-07-15
dc.date.accessioned2026-07-07T09:50:27Z
dc.date.available2026-07-07T09:50:27Z
dc.descriptionWe describe three methods to determine a faithful representation of small dimension for a finite-dimensional nilpotent Lie algebra over an arbitrary field. We apply our methods in finding bounds for the smallest dimension $μ(\Lg)$ of a faithful $\Lg$-module for some nilpotent Lie algebras $\Lg$. In particular, we describe an infinite family of filiform nilpotent Lie algebras $\Lf_n$ of dimension $n$ over $\Q$ and conjecture that $μ(\Lf_n) > n+1$. Experiments with our algorithms suggest that $μ(\Lf_n)$ is polynomial in $n$.
dc.description14 pages
dc.identifierhttps://arxiv.org/abs/0807.2345
dc.identifierhttp://arxiv.org/abs/0807.2345
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/164949
dc.subjectRepresentation Theory
dc.subjectRings and Algebras
dc.titleComputing faithful representations for nilpotent Lie algebras
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