Invariant Poisson Realizations and the Averaging of Dirac Structures

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2014
• Main Authors: Vallejo, J.A., Vorobiev, Y.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2014
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/146597
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Invariant Poisson Realizations and the Averaging of Dirac Structures / J.A. Vallejo, Y. Vorobiev // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 29 назв. — англ.

We describe an averaging procedure on a Dirac manifold, with respect to a class of compatible actions of a compact Lie group. Some averaging theorems on the existence of invariant realizations of Poisson structures around (singular) symplectic leaves are derived. We show that the construction of cou...