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The Fock-Rosly Poisson Structure as Defined by a Quasi-Triangular r-Matrix
Репозиторій DSpace/Manakin
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2017, том 13
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The Fock-Rosly Poisson Structure as Defined by a Quasi-Triangular r-Matrix
Інший ID:
2010 Mathematics Subject Classification: 53D17; 53D30; 17B62
DOI:10.3842/SIGMA.2017.063
DOI:10.3842/SIGMA.2017.063
Посилання:
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.
Підтримка:
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.
Дата:
2017
Переглядів:
489
Завантажень:
226
Анотація:
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.
