Journal of Lie Theory 18 (2008), No. 2, 335--350
Copyright Heldermann Verlag 2008
On Filiform and 2-Filiform Leibniz Algebras of Maximum Length
Jesús M. Cabezas
Dpto. de Matemática Aplicada, Universidad del País Vasco, C/ Nieves Cano 12, 01006 Vitoria Alava, Spain
jm.cabezas@ehu.es
Luisa Maria Camacho
Dpto. Matemática Aplicada I, Universidad de Sevilla, Avda. Reina Mercedes s/n, 41012 Sevilla, Spain
lcamacho@us.es
Isabel M. Rodríguez
Dpto. de Matemáticas, Universidad de Huelva, Ctra. de Palos de la Frontera s/n, 21071 Rábida Huelva, Spain
rodgar@uhu.es
Leibniz algebras appear as a generalization of Lie algebras. The classification of naturally graded p-filiform Lie algebras is known. Several authors have studied the naturally graded p-filiform Leibniz algebras for any p with p ≥ 0.
J. R. Gómez, A. Jiménez-Merchán and J. Reyes ["Filiform Lie algebras of maximum length", Extracta Mathematicae 16 (2001) 405--421] have investigated families of nilpotent Lie algebras with other types of non-natural gradation, a gradation with a large number of subspaces. The algebras with maximum number of subspaces in the gradation will be called maximum length algebras.
We deal with the classification of filiform and 2-filiform Leibniz algebras of maximum length.
Keywords: Leibniz algebras, naturally graded algebras.
MSC: 17A32, 17B30
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