The Classification of Naturally Graded p-Filiform Leibniz Algebras

Abstract

In the present article the classification of n-dimensional naturally graded p-filiform (1 ≤ p ≤ n − 4) Leibniz algebras is obtained. A splitting of the set of naturally graded Leibniz algebras into the families of Lie and non Lie Leibniz algebras by means of characteristic sequences (isomorphism invariants) is proved.

Key Words:

• Characteristic sequence
• Leibniz algebra
• Lie algebra
• Natural gradation
• Nilpotence
• p-Filiformlicity

2000 Mathematics Subject Classification:

• 17A32
• 17A36
• 17A60
• 17B70

ACKNOWLEDGMENTS

This work is supported in part by the PAICYT, FQM143 of the Junta de Andalucía (Spain). The last author was supported by grant of INTAS Ref. No. 0483-3035, and he is very grateful to hospitality of Universidad de Sevilla.

Notes

Communicated by A. Elduque.