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...
Gespeichert in:
| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2014 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2014
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/146597 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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| _version_ | 1862740550114869248 |
|---|---|
| author | Vallejo, J.A. Vorobiev, Y. |
| author_facet | Vallejo, J.A. Vorobiev, Y. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
|
| first_indexed | 2025-12-07T20:15:51Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146597 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T20:15:51Z |
| publishDate | 2014 |
| publisher | Інститут математики НАН України |
| 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 |
| spellingShingle | Invariant Poisson Realizations and the Averaging of Dirac Structures Vallejo, J.A. Vorobiev, Y. |
| title | 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_short | Invariant Poisson Realizations and the Averaging of Dirac Structures |
| title_sort | invariant poisson realizations and the averaging of dirac structures |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146597 |
| work_keys_str_mv | AT vallejoja invariantpoissonrealizationsandtheaveragingofdiracstructures AT vorobievy invariantpoissonrealizationsandtheaveragingofdiracstructures |