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Invariant Poisson Realizations and the Averaging of Dirac Structures
Репозиторій DSpace/Manakin
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- Фізико-технічні та математичні науки
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- Відділення математики
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2014, том 10
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Invariant Poisson Realizations and the Averaging of Dirac Structures
Інший ID:
2010 Mathematics Subject Classification: 53D17; 70G45; 53C12
DOI:10.3842/SIGMA.2014.096
DOI:10.3842/SIGMA.2014.096
Посилання:
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.
Підтримка:
The first author (JAV) was partially supported by the Mexican Consejo Nacional de Ciencia
y Tecnolog´ıa (CONACyT) research project CB-2012 179115. Both authors acknowledge the
detailed comments of the referees, which helped to improve the contents and presentation of
this paper.
Дата:
2014
Переглядів:
495
Завантажень:
236
Анотація:
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 coupling Dirac structures (invariant with respect to locally Hamiltonian group actions) on a Poisson foliation is related with a special class of exact gauge transformations.
