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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2018 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2018
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/209459 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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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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 |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Poisson Geometry Related to Atiyah Sequences |
| spellingShingle |
Poisson Geometry Related to Atiyah Sequences Mackenzie, K. Odzijewicz, A. Sliżewska, A. |
| title_short |
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_sort |
poisson geometry related to atiyah sequences |
| author |
Mackenzie, K. Odzijewicz, A. Sliżewska, A. |
| author_facet |
Mackenzie, K. Odzijewicz, A. Sliżewska, A. |
| publishDate |
2018 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| 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.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/209459 |
| 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. |
| work_keys_str_mv |
AT mackenziek poissongeometryrelatedtoatiyahsequences AT odzijewicza poissongeometryrelatedtoatiyahsequences AT slizewskaa poissongeometryrelatedtoatiyahsequences |
| first_indexed |
2025-12-07T13:14:19Z |
| last_indexed |
2025-12-07T13:14:19Z |
| _version_ |
1850885966997225472 |