Mathematics – Representation Theory
Scientific paper
2008-07-15
Mathematics
Representation Theory
14 pages
Scientific paper
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 $n$.
Burde Dietrich
Eick Bettina
Graaf Willem de
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