Integrability of quotients in Poisson and Dirac geometry

TL;DR

This paper investigates the conditions under which Poisson and Dirac structures derived from quotient constructions are integrable, providing new insights and explicit constructions of related Lie groupoids.

Contribution

It introduces new criteria for integrability of quotient Poisson and Dirac structures and constructs explicit Lie groupoids for specific classes of homogeneous spaces.

Findings

Classical results on integrability are recovered.

New applications to quotient structures are demonstrated.

Explicit Lie groupoid constructions for certain homogeneous spaces are provided.

Abstract

We study the integrability of Poisson and Dirac structures that arise from quotient constructions. From our results we deduce several classical results as well as new applications. We also give explicit constructions of Lie groupoids integrating two interesting families of geometric structures: (i) a special class of Poisson homogeneous spaces of symplectic groupoids integrating Poisson groups and (ii) Dirac homogeneous spaces.