%0 Journal Article
%T Computing faithful representations for nilpotent Lie algebras
%A Dietrich Burde
%A Bettina Eick
%A Willem de Graaf
%J Mathematics
%D 2008
%I arXiv
%X We 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 $\mu(\Lg)$ 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 $\mu(\Lf_n) > n+1$. Experiments with our algorithms suggest that $\mu(\Lf_n)$ is polynomial in $n$.
%U http://arxiv.org/abs/0807.2345v1