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3-filiform Lie algebras of dimension 8. (English) Zbl 0942.17003
The (nilpotent) \(p\)-filiform Lie algebras were introduced by J. M. Cabezas, J. R. Gómez and A. Jiménez-Merchan [Algebra and operator theory, Pro. Colloq., Tashkent 1997, 93-102 (1998; Zbl 0924.17005)] and the difficulty of classification of such algebras seems to be a nonincreasing function of \(p\). The classification problem of \(p\)-filiform Lie algebras of dimension \(n\) was solved for \(p\geq n-3\) in the above cited paper, and for \(p=n-4\) by J. M. Cabezas and J. R. Gómez [Commun. Algebra 27, 4803-4819 (1999; Zbl 0934.17003)]. The aim of the paper under review is to solve the problem for \(p=n-5\) in the case \(n=8\), thus completing previous results obtained by J. M. Cabezas jointly with the present authors [A class of nilpotent Lie algebras, Commun. Algebra (to appear)].
The proofs are carefully carried out for all possible values of the dimensions of center and derived algebra. One can remark here the detailed description of the invariants that are needed in order to distinguish the different isomorphism classes of Lie algebras.

MSC:
17B30 Solvable, nilpotent (super)algebras
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References:
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