The modular class of a Dirac map

TL;DR

This paper investigates the modular classes of Dirac manifolds and maps, exploring their properties and applications to Poisson reduction under Poisson Lie group actions.

Contribution

It introduces the concept of modular classes for Dirac maps and analyzes their role in Poisson manifold reduction processes.

Findings

Modular classes of Dirac manifolds are characterized and related to Dirac maps.

The relationship between modular classes and Poisson reduction is clarified.

Applications to Poisson Lie group actions are demonstrated.

Abstract

In this paper we study the modular classes of Dirac manifolds and of Dirac maps, and we discuss their basic properties. We apply these results to explain the relationship between the modular classes of the various structures involved in the reduction of a Poisson manifold under the action by of a Poisson Lie group.