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Since the introduction of the concept of isotopism of algebras by Albert in1942, a prolific literature on the subject has been developed for distincttypes of algebras. Nevertheless, there barely exists any result on the problemof distributing Lie algebras into isotopism classes. The current paper is afirst step to deal with such a problem. Specifically, we define a new series ofisotopism invariants and we determine explicitly the distribution intoisotopism classes of $n$-dimensional filiform Lie algebras, for $n\leq 7$. Wealso deal with the distribution of such algebras into isomorphism classes, forwhich we confirm some known results and we prove that there exist $p+8$isomorphism classes of seven-dimensional filiform Lie algebras over the finitefield $\mathbb{F}_p$ if $p\neq 2$.

Isomorphism and isotopism classes of filiform Lie algebras of dimension up to seven