3-Filiform Leibniz algebras of maximum length,whose naturally graded algebras are Lie algebras |
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| Authors: | L.M. Camacho E.M. Cañete J.R. Gómez B.A. Omirov |
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| Affiliation: | 1. Departmento de Matemática Aplicada I , Universidad de Sevilla, Avda. Reina Mercedes , Sevilla 41012 s/n, Spain lcamacho@us.es;3. Departmento de Matemática Aplicada I , Universidad de Sevilla, Avda. Reina Mercedes , Sevilla 41012 s/n, Spain;4. Institute of Mathematics and Information Technologies , Uzbekistan Academy of Science , F. Hodjaev str. 29, Tashkent 100125, Uzbekistan |
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| Abstract: | In this article we present the classification of the 3-filiform Leibniz algebras of maximum length, whose associated naturally graded algebras are Lie algebras. Our main tools are a previous existence result by Cabezas and Pastor [J.M. Cabezas and E. Pastor, Naturally graded p-filiform Lie algebras in arbitrary finite dimension, J. Lie Theory 15 (2005), pp. 379–391] and the construction of appropriate homogeneous bases in the connected gradation considered. This is a continuation of the work done in Ref. [J.M. Cabezas, L.M. Camacho, and I.M. Rodríguez, On filiform and 2-filiform Leibniz algebras of maximum length, J. Lie Theory 18 (2008), pp. 335–350]. |
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| Keywords: | Lie algebra Leibniz algebra nilpotence natural gradation characteristic sequence p-filiform maximum length |
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