Braiding for categorical algebras and crossed modules of algebras II: Leibniz algebras

TL;DR

This paper explores braided categorical Leibniz algebras and crossed modules, relating them to Lie algebra structures via the Loday-Pirashvili category, expanding the understanding of algebraic braiding in Leibniz contexts.

Contribution

It introduces the study of braided structures in Leibniz algebras and connects them with Lie algebra counterparts through categorical frameworks.

Findings

Established relationships between braided Leibniz and Lie algebra structures.

Extended categorical frameworks to include Leibniz algebras.

Provided new insights into algebraic braiding in Leibniz contexts.

Abstract

In this paper we study the category of braided categorical Leibniz algebras and braided crossed modules of Leibniz algebras and we relate these structures with the categories of braided categorical Lie algebras and braided crossed modules of Lie algebras using the Loday-Pirashvili category.