Solvable extensions of the naturally graded quasi-filiform Leibniz algebras

Abstract

This work is devoted to the complete classification of solvable Leibniz algebras with the naturally graded quasi-filiform non-Lie nilradical. It should be noted that the class of naturally graded quasi-filiform Leibniz algebras is sufficiently large, and solvable Leibniz algebras with the nilradical which is isomorphic to several of these algebras are classified in a series of works. This paper considered all omitted cases and completed the problem of classifying solvable Leibniz algebras with naturally graded quasi-filiform non-Lie nilradical. At the end of the paper we combine all results obtained to date, and provide a complete list of solvable Leibniz algebras, whose nilradical is a naturally graded quasi-filiform Leibniz algebra.

2020 Mathematics Subject Classification:

• 17A32
• 17A36
• 17A65
• 17B30

Keywords:

• Derivation
• Leibniz algebra
• nilradical
• quasi-filiform
• solvability and nilpotency