Varieties of Nilpotent Complex Leibniz Algebras of Dimension Less than Five

Leibniz algebra deformations of a Lie algebra

“…The classification of complex nilpotent Leibniz algebras up to isomorphism for dimension 2 and 3 is in [7] and [1]. In dimension three there are five non isomorphic algebras and one infinite family of pairwise not isomorphic algebras.…”

Description of some classes of Leibniz algebras

“…It seems the same scheme as above occurs in Leibniz algebras case as well. The counterpart of the problem (1) has been studied in [1,8,[10][11][12][13][14][15] and others. The problem (2) for Leibniz algebras is still remaining untouched.…”

Versal Deformations of Leibniz Algebras

“…Any Lie algebra is automatically a Leibniz algebra, as in the presence of antisymmetry, the Jacobi identity reduces to the Leibniz identity. More examples of Leibniz algebras were given in [20], and recently for instance in [1,2].…”