Author(s)

J.R. Gomez, A. Jimenez-Merchan & Y. Khakimdjanov

Abstract

We show how the features of Mathematica can be used in the classification of the filiform Lie algebras. We reduce the parameters which define a family of filiform Lie algebras until its different orbits can be determined by choosing just one algebra from each of them. 1 Introduction The first non-trivial classifications of some classes of low-dimensional nilpo- tent Lie algebra are due to K. Umlauf. In his thesis [10] (Leipzig, 1891) he presented the list of nilpotent Lie algebras of dimension m < 6. He gave also the list of nilpotent Lie algebras of dimension m < 9 admitting a basis (Ao, Xi, . . . , Xm-i) with [XQ, Xj\ = Xi+i for i = 1, . . . . ra — 2. Now, the nilpotent Lie algebras with this property are called filiform Lie algebras. Umlauf 's list

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