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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Дата:2017
Автор: Mouquin, V.
Формат: Стаття
Мова:English
Опубліковано: Інститут математики НАН України 2017
Назва видання:Symmetry, Integrability and Geometry: Methods and Applications
Онлайн доступ:http://dspace.nbuv.gov.ua/handle/123456789/148752
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати: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
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spelling 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
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language 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
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