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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...
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Інститут математики НАН України
2014
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/146597 |
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irk-123456789-1465972019-02-11T01:24:01Z Invariant Poisson Realizations and the Averaging of Dirac Structures Vallejo, J.A. Vorobiev, Y. 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. 2014 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/146597 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Vallejo, J.A. Vorobiev, Y. |
| spellingShingle |
Vallejo, J.A. Vorobiev, Y. Invariant Poisson Realizations and the Averaging of Dirac Structures Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Vallejo, J.A. Vorobiev, Y. |
| author_sort |
Vallejo, J.A. |
| title |
Invariant Poisson Realizations and the Averaging of Dirac Structures |
| 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 |
| publisher |
Інститут математики НАН України |
| publishDate |
2014 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT vallejoja invariantpoissonrealizationsandtheaveragingofdiracstructures AT vorobievy invariantpoissonrealizationsandtheaveragingofdiracstructures |
| first_indexed |
2023-05-20T17:25:11Z |
| last_indexed |
2023-05-20T17:25:11Z |
| _version_ |
1796153250433466368 |