#### Vol. 311, No. 1, 2021

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Integrability of quotients in Poisson and Dirac geometry

### Daniel Álvarez

Vol. 311 (2021), No. 1, 1–32
DOI: 10.2140/pjm.2021.311.1
##### Abstract

We study the integrability of Poisson and Dirac structures that arise from quotient constructions. As our main general result, we characterize the integrability of Poisson structures which are obtained as quotients of Dirac structures. We illustrate our constructions by deducing several classical results as well as new applications such as an explicit description of Lie groupoids integrating two interesting families of geometric structures:

1. a special class of Poisson homogeneous spaces of symplectic groupoids integrating Poisson groups and
2. Dirac homogeneous spaces.
##### Keywords
Lie groupoids and Lie algebroids, Poisson geometry, Courant algebroids, symplectic groupoids
Primary: 53D17