Abstract
In this paper, we present an algorithmic method to describe and classify filiform Lie algebras by considering the maximal dimension of abelian ideals and studying the relation between them and some known invariants of filiform Lie algebras. To do so, we have proved some new results about structure coefficients in the general law of filiform Lie algebras. Moreover, some mistakes are corrected in the already-known classification of filiform Lie algebras of dimension 8.
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