# Generalized derivations of Hom-Jordan algebras

## TL;DR

This paper investigates the structure of generalized derivation algebras in Hom-Jordan algebras, revealing their decomposition and embedding properties, and exploring centroid characteristics.

## Contribution

It introduces a decomposition of generalized derivations into quasiderivations and quasicentroids, and shows how quasiderivations embed into larger Hom-Jordan algebras.

## Key findings

- $GDer(V) = QDer(V) + QC(V)$ decomposition
- Quasiderivations embed into larger Hom-Jordan algebras
- Develops results on centroids of Hom-Jordan algebras

## Abstract

In this paper, we give some properties of generalized derivation algebras of Hom-Jordan algebras. In particular, we show that $GDer(V) = QDer(V) + QC(V)$, the sum of the quasiderivation algebra and the quasicentroid. We also prove that $QDer(V)$ can be embedded as derivations into a larger Hom-Jordan algebra. General results on centroids of Hom-Jordan algebras are also developed in this paper.