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

We adopt 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 at most~9 over ${\text{F}}_2$ and those of dimension at most~7 over ${\text{F}}_3$ and ${\text{F}}_5$.