About the reducibility of the variety of complex Leibniz algebras

TL;DR

This paper investigates the algebraic structure of Leibniz algebras, demonstrating their varieties are reducible using perturbation and contraction techniques, particularly for dimensions greater than two.

Contribution

It introduces methods to analyze the reducibility of Leibniz algebra varieties, extending concepts from Lie algebra theory.

Findings

Algebraic varieties of Leibniz algebras are reducible for dimensions > 2.

Perturbation and contraction are effective tools for studying Leibniz algebra structures.

The work generalizes known results from Lie algebras to Leibniz algebras.

Abstract

In this paper, using the notions of perturbation and contraction of Lie and Leibniz algebras, we show that the algebraic varieties of Leibniz and nilpotent Leibniz algebras of dimension greater than 2 are reducible.