Equivalent description of Hom-Lie algebroids

TL;DR

This paper explores the properties and equivalent formulations of Hom-Lie algebroids, demonstrating how different definitions can be transformed into each other under certain conditions.

Contribution

It provides a unified framework for understanding Hom-Lie algebroids by establishing equivalences between existing definitions and analyzing their properties.

Findings

Two definitions of Hom-Lie algebroids are shown to be equivalent under specific conditions.

Properties of Hom-Lie algebroids are systematically studied.

The paper offers a new perspective on the structure of Hom-Lie algebroids.

Abstract

In this paper, we study representations of Hom-Lie algebroids, give some properties of Hom-Lie algebroids and discuss equivalent statements of Hom-Lie algebroids. Then, we prove that two known definitions of Hom-Lie algebroids can be transformed into each other under some conditions.