3-Filiform Leibniz algebras of maximum length, whose naturally graded algebras are Lie algebras

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].

Keywords:

• Lie algebra
• Leibniz algebra
• nilpotence
• natural gradation
• characteristic sequence
• p-filiform
• maximum length

AMS Subject Classifications::

• 17A32
• 17A36
• 17A60
• 17B70