Invariant Poisson Realizations and the Averaging of Dirac Structures
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...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2014 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2014
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146597 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-146597 |
|---|---|
| record_format |
dspace |
| spelling |
Vallejo, J.A. Vorobiev, Y. 2019-02-10T09:45:44Z 2019-02-10T09:45:44Z 2014 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. 1815-0659 2010 Mathematics Subject Classification: 53D17; 70G45; 53C12 DOI:10.3842/SIGMA.2014.096 https://nasplib.isofts.kiev.ua/handle/123456789/146597 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. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Invariant Poisson Realizations and the Averaging of Dirac Structures Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Invariant Poisson Realizations and the Averaging of Dirac Structures |
| spellingShingle |
Invariant Poisson Realizations and the Averaging of Dirac Structures Vallejo, J.A. Vorobiev, Y. |
| title_short |
Invariant Poisson Realizations and the Averaging of Dirac Structures |
| title_full |
Invariant Poisson Realizations and the Averaging of Dirac Structures |
| title_fullStr |
Invariant Poisson Realizations and the Averaging of Dirac Structures |
| title_full_unstemmed |
Invariant Poisson Realizations and the Averaging of Dirac Structures |
| title_sort |
invariant poisson realizations and the averaging of dirac structures |
| author |
Vallejo, J.A. Vorobiev, Y. |
| author_facet |
Vallejo, J.A. Vorobiev, Y. |
| publishDate |
2014 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
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.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/146597 |
| citation_txt |
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. |
| work_keys_str_mv |
AT vallejoja invariantpoissonrealizationsandtheaveragingofdiracstructures AT vorobievy invariantpoissonrealizationsandtheaveragingofdiracstructures |
| first_indexed |
2025-12-07T20:15:51Z |
| last_indexed |
2025-12-07T20:15:51Z |
| _version_ |
1850881921426391040 |