Abelian extensions of five-dimensional solvable Leibniz algebras

2025/06/30 by Khudoyberdiyev, A. Kh., Sheraliyeva, S. A.
#17A32 #17A36 #17B30 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2506.23528

Abstract

In this work, we extend the central extension method for solvable Leibniz algebras. Using this method, a complete classification of one-dimensional abelian extensions of five-dimensional solvable Leibniz algebras with a non-trivial three-dimensional nilradical is obtained. Furthermore, we explore extensions of solvable Leibniz algebras whose nilradical is null-filiform, establishing that, in this case, there exists a unique solvable abelian extension.

Citations

• Extensions of solvable Lie algebras with naturally graded filiform nilradical
• On non-abelian extensions of Leibniz algebras
• The classification of 4-dimensional Leibniz algebras
• Classification of solvable Leibniz algebras with null-filiform nilradical
• On Levi's Theorem for Leibniz algebras

Related

• Classification of solvable Leibniz algebras with abelian nilradical and k-1 dimensional extension
• Solvable Leibniz Algebras with Abelian Nilradicals
• Solvable extensions of the naturally graded quasi-filiform Leibniz algebras
• Classification of solvable Leibniz algebras with null-filiform nilradical
• Solvable Leibniz algebras whose nilradical is a quasi-filiform Leibniz algebra of maximum length