Right and left solvable extensions of an associative Leibniz algebra

A sequence of nilpotent Leibniz algebras denoted by Nn,18 is introduced. Here n denotes the dimension of the algebra defined for n≥4; the first term in the sequence is ℛ18 in the list of four-dimensional nilpotent Leibniz algebras introduced by Albeverio et al. [4 Albeverio, S., Omirov, B. A., Rakhimov, I. S. (2006). Classification of 4-dimensional nilpotent complex Leibniz algebras. Extr. Math. 21(3):197–210. [Google Scholar]]. Then all possible right and left solvable indecomposable extensions over the field ℝ are constructed so that Nn,18 serves as the nilradical 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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