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
Mathematical Subject Classification
Primary: 53D17
Milestones
Received: 21 October 2019
Revised: 15 September 2020
Accepted: 11 January 2021
Published: 17 March 2021
Authors
Daniel Álvarez
Departamento de Matemáticas, Facultad de Ciencias
Universidad Nacional Autónoma de México
Mexico City
Mexico