Computing faithful representations for nilpotent Lie algebras
Abstract
We describe three methods to determine a faithful representation of small dimension for a finitedimensional 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 $n$.
 Publication:

arXiv eprints
 Pub Date:
 July 2008
 arXiv:
 arXiv:0807.2345
 Bibcode:
 2008arXiv0807.2345B
 Keywords:

 Mathematics  Representation Theory;
 Mathematics  Rings and Algebras
 EPrint:
 14 pages