Some problems about nilpotent Lie algebras (Q2738445)

The paper under review is a survey, without proofs, of several recent results related to the (still open) classification problem of finite-dimensional complex nilpotent Lie algebras. In the authors' words, the paper is in particular ``an overview of the work developed on Lie theory over the last years by some members of the research group directed by J. R. Gómez''. NEWLINENEWLINENEWLINEThe themes of this research are: filiform and \(p\)-filiform Lie algebras, Lie algebras with small nilindex, naturally graded nilpotent Lie algebras, length of nilpotent Lie algebras, symbolic calculus on Lie algebras. The latter theme has to be emphasized here, since one of the leading ideas of the paper under review is that the computers turn out to be a most effective research tool, both in concretely determining Lie algebras of small dimensions and in suggesting theoretical problems concerning Lie algebras.NEWLINENEWLINEFor the entire collection see [Zbl 0963.00025].