Leibniz Algebras and Lie Algebras

TL;DR

This paper explores the structure of finite-dimensional complex Leibniz algebras, introducing new subclasses and analyzing their subalgebra posets using bilinear pairings, advancing understanding of their algebraic properties.

Contribution

It introduces left central and symmetric Leibniz algebras and studies their subalgebra structures through novel bilinear pairings, providing new insights into Leibniz algebra theory.

Findings

Introduction of left central Leibniz algebras

Definition of symmetric Leibniz algebras

Analysis of the poset of Lie subalgebras

Abstract

This paper concerns the algebraic structure of finite-dimensional complex Leibniz algebras. In particular, we introduce left central and symmetric Leibniz algebras, and study the poset of Lie subalgebras using an associative bilinear pairing taking values in the Leibniz kernel.