Mackenzie, K.C. orcid.org/0000-0002-4697-2513, Odzijewicz, A. and Sliżewska, A. (2018) Poisson Geometry Related to Atiyah Sequences. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 14 (005). ISSN 1815-0659
Abstract
We construct and investigate a short exact sequence of Poisson VB-groupoids which is canonically related to the Atiyah sequence of a G-principal bundle P. Our results include a description of the structure of the symplectic leaves of the Poisson groupoid T∗P×T∗PG⇉T∗PG. The semidirect product case, which is important for applications in Hamiltonian mechanics, is also discussed.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018 The Author(s). Published in SIGMA under the terms of the Creative Commons Attribution-ShareAlike License. |
Keywords: | Atiyah sequence; VB-groupoid; Poisson groupoid; dualization of VB-groupoid |
Dates: |
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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: | 13 Jul 2018 11:17 |
Last Modified: | 14 Jul 2018 01:07 |
Published Version: | https://doi.org/10.3842/SIGMA.2018.005 |
Status: | Published |
Publisher: | National Academy of Science of Ukraine |
Refereed: | Yes |
Identification Number: | 10.3842/SIGMA.2018.005 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:133206 |