Classification of a subclass of low-dimensional complex filiform Leibniz algebras

Abstract

We give a complete classification of a subclass of complex filiform Leibniz algebras obtained from naturally graded non-Lie filiform Leibniz algebras. The isomorphism criteria in terms of invariant functions are given.

Keywords:

• filiform Leibniz algebra
• adapted basis
• invariant
• isomorphism

AMS Subject Classifications::

• 17A32
• 17B30(primary)
• 13A50(secondary)

Acknowledgements

The authors acknowledge MOSTI (Malaysia) for the financial support. They are also grateful to Profs B.A. Omirov and U.D. Bekbaev for helpful discussions. The authors express gratitude to the referee for valuable suggestions and comments in the original version of this article.