Jacobi-Nijenhuis algebroids and their modular classes

TL;DR

This paper introduces Jacobi-Nijenhuis algebroids, a generalization of Poisson-Nijenhuis algebroids, and investigates their modular classes, expanding the understanding of their geometric and algebraic properties.

Contribution

It defines Jacobi-Nijenhuis algebroids and explores their modular classes, providing new insights into their structure and compatibility conditions.

Findings

Jacobi-Nijenhuis algebroids generalize Poisson-Nijenhuis structures.

Modular classes of these algebroids are characterized and studied.

The work extends the theory of algebroid modular classes to a broader context.

Abstract

Jacobi-Nijenhuis algebroids are defined as a natural generalization of Poisson-Nijenhuis algebroids, in the case where there exists a Nijenhuis operator on a Jacobi algebroid which is compatible with it. We study modular classes of Jacobi and Jacobi-Nijenhuis algebroids.