$3$-filiform Leibniz algebras of maximum length

L. M. Camacho^a, E. M. Cañete^a, J. R. Gómez^a, B. A. Omirov<sup>b

a</sup> 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.

UDC: 512.554.38

Received: 14.03.2014

DOI: 10.17377/smzh.2016.57.104

 English version: Siberian Mathematical Journal, 2016, 57:1, 24–35

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