On Jacobi quasi-Nijenhuis algebroids and Courant-Jacobi algebroid morphisms

TL;DR

This paper introduces Jacobi quasi-Nijenhuis algebroids, establishes their connection to quasi-Jacobi bialgebroids and Courant-Jacobi algebroids, and defines morphisms between these structures with illustrative examples.

Contribution

It defines Jacobi quasi-Nijenhuis algebroids and links them to quasi-Jacobi bialgebroids and Courant-Jacobi algebroids, including morphisms and examples.

Findings

Jacobi quasi-Nijenhuis algebroids are associated with quasi-Jacobi bialgebroids.

Any Jacobi quasi-Nijenhuis algebroid yields a Courant-Jacobi algebroid.

Examples of Courant-Jacobi algebroid morphisms are provided.

Abstract

We propose a definition of Jacobi quasi-Nijenhuis algebroid and show that any such Jacobi algebroid has an associated quasi-Jacobi bialgebroid. Therefore, also an associated Courant-Jacobi algebroid is obtained. We introduce the notions of quasi-Jacobi bialgebroid morphism and Courant-Jacobi algebroid morphism providing also some examples of Courant-Jacobi algebroid morphisms.