Journal of Lie Theory 15 (2005), No. 2, 379--391
Copyright Heldermann Verlag 2005
Naturally Graded p-Filiform Lie Algebras in Arbitrary Finite Dimension
J. M. Cabezas
Dpto. Matemática Aplicada, E. U. de Ingeniería, Universidad del País Vasco, Nieves Cano 12, 01006 Vitoria, Spain
mapcamaj@vc.ehu.es
E. Pastor
Dpto. Matemática Aplicada, E. U. de Ingeniería, Universidad del País Vasco, Nieves Cano 12, 01006 Vitoria, Spain
mappasae@vc.ehu.es
[Abstract-pdf]
The present paper offers the classification of naturally graded $p$-filiform Lie algebras in arbitrary finite dimension $n$. For sufficiently high $n$, ($n \geq \max \{3p-1,p+8\}$), and for all admissible value of $p$ the results are a generalization of Vergne's in case of filiform Lie algebras [Vergne, M., Cohomologie des alg\`ebres de Lie nilpotentes. Application \`a l'\'etude de la variet\'e des alg\`ebres de Lie nilpotentes, Bull. Soc. Math. France 98 (1970) 81--116].
Keywords: Nilpotent Lie algebra, filiform, naturally graded.
MSC: 22E60, 17B30; 17B70
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