A computer-based approach to the classification of nilpotent Lie algebras

Abstract

We adapt the $p$-group generation algorithm to classify small-dimensional nilpotent Lie algebras over small fields. Using an implementation of this algorithm, we list the nilpotent Lie algebras of dimension up to 9 over $\F_2$ and those of dimension up to 7 over $\F_3$ and $\F_5$.