Existentially closed Leibniz algebras and an embedding theorem

Abstract

In this paper we introduce the notion of existentially closed Leibniz algebras. Then we use HNN-extensions of Leibniz algebras in order to prove an embedding theorem.

The algebraic and geometric classification of nilpotent binary and mono Leibniz algebras

“…A systematic study of algebraic properties of Leibniz algebras is started from the Loday paper. So, several classical theorems from Lie algebras theory have been extended to the Leibniz algebras case; many classification results regarding nilpotent, solvable, simple, and semisimple Leibniz algebras are obtained (see, for example, [4,7,14,32,33,40,44,47,50] and references therein). Leibniz algebras is a particular case of terminal algebras and, on the other hand, symmetric Leibniz algebras are Poisson admissible algebras.…”

Operadic approach to HNN-extensions of Leibniz algebras

“…Leibniz algebras are non-antisymmetric generalization of Lie algebras introduced by Bloh [2] and Loday [13], [14], and they have many applications in both pure and applied mathematics and in physics. Because of this, many known results of the theory of Lie algebras as well as combinatorial group theory have been extended to Leibniz algebras in the last two decades (see, for instance, [1], [10] and [20]. )…”