On some properties of $\mathsf{Lie}$-centroids of Leibniz algebras

TL;DR

This paper investigates properties of Lie-centroids in Leibniz algebras, focusing on derivations and their generalizations, and computes the Lie-centroid of tensor products involving Leibniz algebras.

Contribution

It introduces new insights into Lie-centroids of Leibniz algebras, including their relations to derivations and the structure of tensor products.

Findings

Characterization of Lie-centroids related to derivations

Determination of Lie-centroid of tensor products

Analysis of generalized and almost inner Lie-derivations

Abstract

We study some properties on $\mathsf{Lie}$-centroids related to central $\mathsf{Lie}$-derivations, generalized $\mathsf{Lie}$-derivations and almost inner $\mathsf{Lie}$-derivations. We also determine the $\mathsf{Lie}$-centroid of the tensor product of a commutative associative algebra and a Leibniz algebra.