Solvable extensions of the naturally graded quasi-filiform Leibniz algebra of second type ℒ²

ABSTRACT

For a sequence of the naturally graded quasi-filiform Leibniz algebra of second type ℒ² introduced by Camacho, Gómez, González and Omirov, all possible right and left solvable indecomposable extensions over the field ℝ are constructed so that the algebra serves as the nilradical of the corresponding solvable Leibniz algebras we find in the paper.

KEYWORDS:

• Derivation
• Leibniz algebra
• nil-independence
• nilpotency
• nilradical
• solvability

AMS SUBJECT CLASSIFICATION:

• 17A30
• 17A32
• 17A36
• 17A60
• 17B30

Notes

¹In the overview we only mention if the algebra is left, otherwise it is right.

²When we work with the left Leibniz algebras, we first change the right multiplication operator to the left everywhere and the right Leibniz identity to the left Leibniz identity in step (iii). We also interchange s and r on the very left in steps (i) and (ii) as well.