Leibniz algebras whose solvable ideal is the maximal extension of the nilradical

2022/03/31 by Abdurasulov, K. K., Shermatova, Z. Kh.
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2203.16967

Abstract

The paper is devoted to the so-called complete Leibniz algebras. It is known that a Lie algebra with a complete ideal is split. We will prove that this result is valid for Leibniz algebras whose complete ideal is a solvable algebra such that the codimension of nilradical is equal to the number of generators of the nilradical.

Related

• On some solvable Leibniz algebras and their completeness
• Maximal solvable Leibniz algebras whose nilradical is a quasi-filiform algebra
• Solvable Leibniz algebras whose nilradical is a quasi-filiform Leibniz algebra of maximum length
• Classification of solvable Leibniz algebras with null-filiform nilradical
• Solvable Leibniz Algebras with Abelian Nilradicals