Classification of 4-dimensional nilpotent complex Leibniz algebras

Abstract

The Leibniz algebras appeared as a generalization of the Lie algebras. In this work we deal with the classification of nilpotent complex Leibniz algebras of low dimensions. Namely, the classification of nilpotent complex Leibniz algebras dimensions less than 3 is extended to the dimension four. {\it AMS Subject Classifications}: 16D70, 17A30, 17A60, 17B30 {\it Key words:} Leibniz algebra, associative algebra, nilpotence, nulfiliform Leibniz algebra, filiform Leibniz algebra.

9 pages

Cited by in corpus (8)

• Degenerations of Zinbiel and nilpotent Leibniz algebras
• Leibniz bialgebras, classical Yang-Baxter equations and dynamical systems
• Classification of some Solvable Leibniz Algebras
• Classification of algebras of level two in the variety of nilpotent algebras and Leibniz algebras
• Hom-Lie-Yamaguti structures on Hom-Leibniz algebras
• Solvable extensions of the naturally graded quasi-filiform Leibniz algebra of second type ${\mathcal{L}}^2$
• Solvable extensions of the naturally graded quasi-filiform Leibniz algebra of second type ${\mathcal{L}}^4$
• Solvable Leibniz algebras with triangular nilradical