Rota-Baxter Operators on 3-Dimensional Lie Algebras and the Classical R-Matrices
Our aim is to classify the Rota-Baxter operators of weight 0 on the 3-dimensional Lie algebra whose derived algebra’s dimension is 2. We explicitly determine all Rota-Baxter operators (of weight zero) on the 3-dimensional Lie algebras g. Furthermore, we give the corresponding solutions of the classi...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2017/6128102 |
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| author | Linli Wu Mengping Wang Yongsheng Cheng |
| author_facet | Linli Wu Mengping Wang Yongsheng Cheng |
| author_sort | Linli Wu |
| collection | DOAJ |
| description | Our aim is to classify the Rota-Baxter operators of weight 0 on the 3-dimensional Lie algebra whose derived algebra’s dimension is 2. We explicitly determine all Rota-Baxter operators (of weight zero) on the 3-dimensional Lie algebras g. Furthermore, we give the corresponding solutions of the classical Yang-Baxter equation in the 6-dimensional Lie algebras g ⋉ad⁎ g⁎ and the induced left-symmetry algebra structures on g. |
| format | Article |
| id | doaj-art-de61c5ca719c4f7a9a8c93d5381e28c6 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-de61c5ca719c4f7a9a8c93d5381e28c62025-08-20T03:26:16ZengWileyAdvances in Mathematical Physics1687-91201687-91392017-01-01201710.1155/2017/61281026128102Rota-Baxter Operators on 3-Dimensional Lie Algebras and the Classical R-MatricesLinli Wu0Mengping Wang1Yongsheng Cheng2School of Mathematics and Statistics, Henan University, Kaifeng 475004, ChinaSchool of Mathematics and Statistics, Henan University, Kaifeng 475004, ChinaSchool of Mathematics and Statistics, Henan University, Kaifeng 475004, ChinaOur aim is to classify the Rota-Baxter operators of weight 0 on the 3-dimensional Lie algebra whose derived algebra’s dimension is 2. We explicitly determine all Rota-Baxter operators (of weight zero) on the 3-dimensional Lie algebras g. Furthermore, we give the corresponding solutions of the classical Yang-Baxter equation in the 6-dimensional Lie algebras g ⋉ad⁎ g⁎ and the induced left-symmetry algebra structures on g.http://dx.doi.org/10.1155/2017/6128102 |
| spellingShingle | Linli Wu Mengping Wang Yongsheng Cheng Rota-Baxter Operators on 3-Dimensional Lie Algebras and the Classical R-Matrices Advances in Mathematical Physics |
| title | Rota-Baxter Operators on 3-Dimensional Lie Algebras and the Classical R-Matrices |
| title_full | Rota-Baxter Operators on 3-Dimensional Lie Algebras and the Classical R-Matrices |
| title_fullStr | Rota-Baxter Operators on 3-Dimensional Lie Algebras and the Classical R-Matrices |
| title_full_unstemmed | Rota-Baxter Operators on 3-Dimensional Lie Algebras and the Classical R-Matrices |
| title_short | Rota-Baxter Operators on 3-Dimensional Lie Algebras and the Classical R-Matrices |
| title_sort | rota baxter operators on 3 dimensional lie algebras and the classical r matrices |
| url | http://dx.doi.org/10.1155/2017/6128102 |
| work_keys_str_mv | AT linliwu rotabaxteroperatorson3dimensionalliealgebrasandtheclassicalrmatrices AT mengpingwang rotabaxteroperatorson3dimensionalliealgebrasandtheclassicalrmatrices AT yongshengcheng rotabaxteroperatorson3dimensionalliealgebrasandtheclassicalrmatrices |