Poisson Geometry Related to Atiyah Sequences

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*P/G⇉T*P/G. The semidirect product case,...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2018
Main Authors: Mackenzie, K., Odzijewicz, A., Sliżewska, A.
Format: Article
Language:English
Published: Інститут математики НАН України 2018
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/209459
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Poisson Geometry Related to Atiyah Sequences / K. Mackenzie, A. Odzijewicz, A. Sliżewska // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 12 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Mackenzie, K.
Odzijewicz, A.
Sliżewska, A.
author_facet Mackenzie, K.
Odzijewicz, A.
Sliżewska, A.
citation_txt Poisson Geometry Related to Atiyah Sequences / K. Mackenzie, A. Odzijewicz, A. Sliżewska // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 12 назв. — англ.
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description 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*P/G⇉T*P/G. The semidirect product case, which is important for applications in Hamiltonian mechanics, is also discussed.
first_indexed 2025-12-07T13:14:19Z
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2025-12-07T13:14:19Z
publishDate 2018
publisher Інститут математики НАН України
record_format dspace
spelling Mackenzie, K.
Odzijewicz, A.
Sliżewska, A.
2025-11-21T19:14:21Z
2018
Poisson Geometry Related to Atiyah Sequences / K. Mackenzie, A. Odzijewicz, A. Sliżewska // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 12 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 58H05; 22A22; 53D17
arXiv: 1506.03216
https://nasplib.isofts.kiev.ua/handle/123456789/209459
https://doi.org/10.3842/SIGMA.2018.005
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*P/G⇉T*P/G. The semidirect product case, which is important for applications in Hamiltonian mechanics, is also discussed.
We extend our best thanks to the referees, who caught many slips and obscurities.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Poisson Geometry Related to Atiyah Sequences
Article
published earlier
spellingShingle Poisson Geometry Related to Atiyah Sequences
Mackenzie, K.
Odzijewicz, A.
Sliżewska, A.
title Poisson Geometry Related to Atiyah Sequences
title_full Poisson Geometry Related to Atiyah Sequences
title_fullStr Poisson Geometry Related to Atiyah Sequences
title_full_unstemmed Poisson Geometry Related to Atiyah Sequences
title_short Poisson Geometry Related to Atiyah Sequences
title_sort poisson geometry related to atiyah sequences
url https://nasplib.isofts.kiev.ua/handle/123456789/209459
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