ABSTRACT
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. [Citation4]. 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.
Notes
1 When we say a Leibniz algebra, we mean a right Leibniz algebra, unless the choice is understood from the context.
2When we work with the left Leibniz algebras, we interchange s and r in step (i) and (ii), the right multiplication operator to the left, and the right Leibniz identity to the left Leibniz identity in step (iii)