LINEARIZATION OF POISSON–LIE STRUCTURES ON THE 2D EUCLIDEAN AND (1 + 1) POINCARÉ GROUPS
The paper deals with linearization problem of Poisson-Lie structures on the \((1+1)\) Poincaré and \(2D\) Euclidean groups. We construct the explicit form of linearizing coordinates of all these Poisson-Lie structures. For this, we calculate all Poisson-Lie structures on these two groups mentioned...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin.
2021-12-01
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| Series: | Ural Mathematical Journal |
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| Online Access: | https://umjuran.ru/index.php/umj/article/view/272 |
| _version_ | 1818502958730444800 |
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| author | Bousselham Ganbouri Mohamed Wadia Mansouri |
| author_facet | Bousselham Ganbouri Mohamed Wadia Mansouri |
| author_sort | Bousselham Ganbouri |
| collection | DOAJ |
| description | The paper deals with linearization problem of Poisson-Lie structures on the \((1+1)\) Poincaré and \(2D\) Euclidean groups. We construct the explicit form of linearizing coordinates of all these Poisson-Lie structures. For this, we calculate all Poisson-Lie structures on these two groups mentioned above, through the correspondence with Lie Bialgebra structures on their Lie algebras which we first determine. |
| first_indexed | 2024-12-10T21:17:20Z |
| format | Article |
| id | doaj.art-565da38942ad4b058fbd063a3f78896e |
| institution | Directory Open Access Journal |
| issn | 2414-3952 |
| language | English |
| last_indexed | 2024-12-10T21:17:20Z |
| publishDate | 2021-12-01 |
| publisher | Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin. |
| record_format | Article |
| series | Ural Mathematical Journal |
| spelling | doaj.art-565da38942ad4b058fbd063a3f78896e2022-12-22T01:33:15ZengKrasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin.Ural Mathematical Journal2414-39522021-12-017210.15826/umj.2021.2.002134LINEARIZATION OF POISSON–LIE STRUCTURES ON THE 2D EUCLIDEAN AND (1 + 1) POINCARÉ GROUPSBousselham Ganbouri0Mohamed Wadia Mansouri1Mohammed First University, Mohammed V Avenue, P.O. Box 524, 60000 OujdaIbn Tofail University, P.O. Box 242, 14000 KénitraThe paper deals with linearization problem of Poisson-Lie structures on the \((1+1)\) Poincaré and \(2D\) Euclidean groups. We construct the explicit form of linearizing coordinates of all these Poisson-Lie structures. For this, we calculate all Poisson-Lie structures on these two groups mentioned above, through the correspondence with Lie Bialgebra structures on their Lie algebras which we first determine.https://umjuran.ru/index.php/umj/article/view/272poisson-lie groups, lie bialgebras, linearization. |
| spellingShingle | Bousselham Ganbouri Mohamed Wadia Mansouri LINEARIZATION OF POISSON–LIE STRUCTURES ON THE 2D EUCLIDEAN AND (1 + 1) POINCARÉ GROUPS Ural Mathematical Journal poisson-lie groups, lie bialgebras, linearization. |
| title | LINEARIZATION OF POISSON–LIE STRUCTURES ON THE 2D EUCLIDEAN AND (1 + 1) POINCARÉ GROUPS |
| title_full | LINEARIZATION OF POISSON–LIE STRUCTURES ON THE 2D EUCLIDEAN AND (1 + 1) POINCARÉ GROUPS |
| title_fullStr | LINEARIZATION OF POISSON–LIE STRUCTURES ON THE 2D EUCLIDEAN AND (1 + 1) POINCARÉ GROUPS |
| title_full_unstemmed | LINEARIZATION OF POISSON–LIE STRUCTURES ON THE 2D EUCLIDEAN AND (1 + 1) POINCARÉ GROUPS |
| title_short | LINEARIZATION OF POISSON–LIE STRUCTURES ON THE 2D EUCLIDEAN AND (1 + 1) POINCARÉ GROUPS |
| title_sort | linearization of poisson lie structures on the 2d euclidean and 1 1 poincare groups |
| topic | poisson-lie groups, lie bialgebras, linearization. |
| url | https://umjuran.ru/index.php/umj/article/view/272 |
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