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Sibirsk. Mat. Zh., 2016, Volume 57, Number 1, Pages 33–46 (Mi smj2727)  

$3$-filiform Leibniz algebras of maximum length

L. M. Camachoa, E. M. Cañetea, J. R. Gómeza, B. A. Omirovb

a University of Seville, Seville, Spain
b Institute of Mathematics and Information Technologies, National University of Uzbekistan, Tashkent, Uzbekistan

Abstract: We complete the description of $3$-filiform Leibniz algebras of maximum length. Moreover, using the good structure of algebras of maximum length, we study some of their cohomological properties. Our main tools are the previous results by Cabezas and Pastor [1], the construction of an appropriate homogeneous basis in the considered connected gradation and the computational support provided by two programs implemented in Mathematica.

Keywords: Lie algebra, Leibniz algebra, nilpotency, natural gradation, characteristic sequence, $p$-filiform algebra, maximum length, cohomology.

Funding Agency Grant Number
Ministerio de Ciencia e Innovación de España MTM2013-43687-P
Coordenaҫão de Aperfeiҫoamento de Pessoal de Nível Superior PNPD/2009-CAPES
This work was supported by Ministerio de Economía y Competitividad (Spain), grant MTM2013-43687-P (European FEDER support included) and by PNPD/2009-CAPES (Brazil).


DOI: https://doi.org/10.17377/smzh.2016.57.104

Full text: PDF file (237 kB)
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English version:
Siberian Mathematical Journal, 2016, 57:1, 24–35

Bibliographic databases:

UDC: 512.554.38
Received: 14.03.2014

Citation: L. M. Camacho, E. M. Cañete, J. R. Gómez, B. A. Omirov, “$3$-filiform Leibniz algebras of maximum length”, Sibirsk. Mat. Zh., 57:1 (2016), 33–46; Siberian Math. J., 57:1 (2016), 24–35

Citation in format AMSBIB
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\paper $3$-filiform Leibniz algebras of maximum length
\jour Sibirsk. Mat. Zh.
\yr 2016
\vol 57
\issue 1
\pages 33--46
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\jour Siberian Math. J.
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\vol 57
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\pages 24--35
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