The modular class of a twisted Poisson structure

TL;DR

This paper explores the properties of twisted Poisson structures on Lie algebroids, defining their modular class and providing explicit representatives, especially for twisted Poisson manifolds.

Contribution

It introduces the concept of the modular class for twisted Poisson structures and explicitly determines representatives, advancing understanding of their geometric and algebraic features.

Findings

Defined the modular class for twisted Poisson structures

Explicitly determined representatives of the modular class

Analyzed properties in the case of twisted Poisson manifolds

Abstract

We study the geometric and algebraic properties of the twisted Poisson structures on Lie algebroids, leading to a definition of their modular class and to an explicit determination of a representative of the modular class, in particular in the case of a twisted Poisson manifold.