Hom-Lie algebroids

TL;DR

This paper introduces hom-Lie algebroids, establishing their equivalence with hom-Gerstenhaber algebras, and provides various examples including hom-Poisson structures, expanding the theoretical framework of generalized algebraic structures.

Contribution

It defines hom-Lie algebroids and demonstrates their correspondence with hom-Gerstenhaber algebras, along with presenting multiple examples such as hom-Poisson structures.

Findings

Hom-Lie algebroids are equivalent to hom-Gerstenhaber algebras.

Several examples of hom-Lie algebroids, including hom-Poisson structures.

Theoretical foundation linking hom-Lie algebroids and hom-Gerstenhaber algebras.

Abstract

We define hom-Lie algebroids, a definition that may seem cumbersome at first, but which is justified, first, by a one-to-one corespondence with hom-Gerstenhaber algebras, a notion that we also introduce, and several examples, including hom-Poisson structures.