On Nilpotent and Simple Leibniz Algebras

Derivations of second type of algebra of second class filiform Leibniz algebras of dimension derivation (n+2)

“…(see [8]) A Leibniz algebra L is said to be nilpotent if there exists s ∈ N such that L 1 ⊃ L 2 ⊃ · · · ⊃ L s = 0. Definition 2.3.…”

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].…”

An Example of Constructing Versal Deformation for Leibniz Algebras

“…Any Lie algebra is automatically a Leibniz algebra, as in the presence of antisymmetry, the Jacobi identity is equivalent to the Leibniz identity. More examples of Leibniz algebras were given in [10,13], and recently for instance in [3,1,2].…”