Solvable extensions of naturally graded quasi-filiform Leibniz algebras of second type <i>ℒ</i>¹ and <i>ℒ</i>³

For sequences of naturally graded quasi-filiform Leibniz algebras of second type ℒ1 and ℒ3 introduced by Camacho et al., all possible right and left solvable indecomposable extensions over the field ℝ are constructed so that these algebras serve as the nilradicals of the corresponding solvable algebras. The construction continues Winternitz’ and colleagues’ program established to classify solvable Lie algebras using special properties rather than trying to extend one dimension at a time.

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