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The Fock-Rosly Poisson Structure as Defined by a Quasi-Triangular r-Matrix
We reformulate the Poisson structure discovered by Fock and Rosly on moduli spaces of flat connections over marked surfaces in the framework of Poisson structures defined by Lie algebra actions and quasitriangular r-matrices, and we show that it is an example of a mixed product Poisson structure ass...
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Інститут математики НАН України
2017
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/148752 |
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irk-123456789-1487522019-02-19T01:27:13Z The Fock-Rosly Poisson Structure as Defined by a Quasi-Triangular r-Matrix Mouquin, V. We reformulate the Poisson structure discovered by Fock and Rosly on moduli spaces of flat connections over marked surfaces in the framework of Poisson structures defined by Lie algebra actions and quasitriangular r-matrices, and we show that it is an example of a mixed product Poisson structure associated to pairs of Poisson actions, which were studied by J.-H. Lu and the author. The Fock-Rosly Poisson structure corresponds to the quasi-Poisson structure studied by Massuyeau, Turaev, Li-Bland, and Ševera under an equivalence of categories between Poisson and quasi-Poisson spaces. 2017 Article The Fock-Rosly Poisson Structure as Defined by a Quasi-Triangular r-Matrix / V. Mouquin // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 10 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 53D17; 53D30; 17B62 DOI:10.3842/SIGMA.2017.063 http://dspace.nbuv.gov.ua/handle/123456789/148752 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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English |
| description |
We reformulate the Poisson structure discovered by Fock and Rosly on moduli spaces of flat connections over marked surfaces in the framework of Poisson structures defined by Lie algebra actions and quasitriangular r-matrices, and we show that it is an example of a mixed product Poisson structure associated to pairs of Poisson actions, which were studied by J.-H. Lu and the author. The Fock-Rosly Poisson structure corresponds to the quasi-Poisson structure studied by Massuyeau, Turaev, Li-Bland, and Ševera under an equivalence of categories between Poisson and quasi-Poisson spaces. |
| format |
Article |
| author |
Mouquin, V. |
| spellingShingle |
Mouquin, V. The Fock-Rosly Poisson Structure as Defined by a Quasi-Triangular r-Matrix Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Mouquin, V. |
| author_sort |
Mouquin, V. |
| title |
The Fock-Rosly Poisson Structure as Defined by a Quasi-Triangular r-Matrix |
| title_short |
The Fock-Rosly Poisson Structure as Defined by a Quasi-Triangular r-Matrix |
| title_full |
The Fock-Rosly Poisson Structure as Defined by a Quasi-Triangular r-Matrix |
| title_fullStr |
The Fock-Rosly Poisson Structure as Defined by a Quasi-Triangular r-Matrix |
| title_full_unstemmed |
The Fock-Rosly Poisson Structure as Defined by a Quasi-Triangular r-Matrix |
| title_sort |
fock-rosly poisson structure as defined by a quasi-triangular r-matrix |
| publisher |
Інститут математики НАН України |
| publishDate |
2017 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148752 |
| citation_txt |
The Fock-Rosly Poisson Structure as Defined by a Quasi-Triangular r-Matrix / V. Mouquin // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 10 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT mouquinv thefockroslypoissonstructureasdefinedbyaquasitriangularrmatrix AT mouquinv fockroslypoissonstructureasdefinedbyaquasitriangularrmatrix |
| first_indexed |
2023-05-20T17:31:14Z |
| last_indexed |
2023-05-20T17:31:14Z |
| _version_ |
1796153476170907648 |