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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2017 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2017
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/148752 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862707825980997632 |
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| author | Mouquin, V. |
| author_facet | Mouquin, V. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-12-07T17:07:54Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-148752 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:07:54Z |
| publishDate | 2017 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Mouquin, V. 2019-02-18T18:25:36Z 2019-02-18T18:25:36Z 2017 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 https://nasplib.isofts.kiev.ua/handle/123456789/148752 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. The author wishes to thank Jiang-Hua Lu, Marco Gualtieri and Francis Bischof f for their helpful comments. The author also wishes to thank the anonymous referees and editors, whose
 suggestions helped improve this paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Fock-Rosly Poisson Structure as Defined by a Quasi-Triangular r-Matrix Article published earlier |
| spellingShingle | The Fock-Rosly Poisson Structure as Defined by a Quasi-Triangular r-Matrix Mouquin, V. |
| title | 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_short | 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148752 |
| work_keys_str_mv | AT mouquinv thefockroslypoissonstructureasdefinedbyaquasitriangularrmatrix AT mouquinv fockroslypoissonstructureasdefinedbyaquasitriangularrmatrix |