On Isomorphisms and Invariants of Finite Dimensional Complex Filiform Leibniz Algebras

Abstract

In this article, we propose an approach classifying a class of filiform Leibniz algebras. The approach is based on algebraic invariants. The method allows to classify all filiform Leibniz algebras (including filiform Lie algebras) in a given fixed dimensional case.

Key Words:

• Filiform Leibniz algebra
• Isomorphism criterion
• Lie algebra
• Natural gradation

2000 Mathematics Subject Classification:

• Primary 17A32, 17A60, 17B30, 17B70
• Secondary 13A50

ACKNOWLEDGMENTS

The research was supported by Grant 06-01-04 SF01-22 MOSTI (Malaysia) and partially by FRGS/FASAI-2007/Sains Tulen/UPM/297 (Malaysia). The authors are grateful to Professor B. A. Omirov for helpful discussions and M. A. Hassan for carrying out calculations for TLb ₅ and TLb ₆. We are also thankful to the referee for valuable comments and suggestions towards the improvement of this work.

Notes

Communicated by I. Shestakov.