Jotz Lean, M. orcid.org/0000-0001-8348-0465 (2016) Homogeneous spaces of Dirac groupoids. Journal of Geometry and Physics , 104. pp. 89-111. ISSN 0393-0440
Abstract
A Poisson structure on a homogeneous space of a Poisson groupoid is homogeneous if the action of the Lie groupoid on the homogeneous space is compatible with the Poisson structures. According to a result of Liu, Weinstein and Xu, Poisson homogeneous spaces of a Poisson groupoid are in correspondence with suitable Dirac structures in the Courant algebroid defined by the Lie bialgebroid of the Poisson groupoid. We show that this correspondence result fits into a more natural context: the one of Dirac groupoids, which are objects generalizing Poisson groupoids and multiplicative closed 2-forms on groupoids.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | © 2016 Elsevier B.V. All rights reserved. This is an author produced version of a paper subsequently published in Journal of Geometry and Physics. Uploaded in accordance with the publisher's self-archiving policy. Article available under the terms of the CC-BY-NC-ND licence (https://creativecommons.org/licenses/by-nc-nd/4.0/) |
Keywords: | Poisson groupoids; Lie groupoids; Dirac manifolds; Homogeneous spaces; Courant algebroids |
Dates: |
|
Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 07 Apr 2016 13:49 |
Last Modified: | 14 Apr 2017 03:32 |
Published Version: | http://dx.doi.org/10.1016/j.geomphys.2016.01.006 |
Status: | Published |
Publisher: | Elsevier |
Refereed: | Yes |
Identification Number: | 10.1016/j.geomphys.2016.01.006 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:97900 |