Poisson Geometry Related to Atiyah Sequences

• 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
• 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.

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,...