Generalized classical Yang-Baxter equation and regular decompositions
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913375030607872 |
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| author | Abedin, Raschid Maximov, Stepan Stolin, Alexander |
| author_facet | Abedin, Raschid Maximov, Stepan Stolin, Alexander |
| contents | The focus of the paper is on constructing new solutions of the generalized classical Yang-Baxter equation (GCYBE) that are not skew-symmetric. Using regular decompositions of finite-dimensional simple Lie algebras, we construct Lie algebra decompositions of $\mathfrak{g}(\!(x)\!) \times \mathfrak{g}[x]/x^m \mathfrak{g}[x]$. The latter decompositions are in bijection with the solutions to the GCYBE. Under appropriate regularity conditions, we obtain a partial classification of such solutions. The paper is concluded with the presentations of the Gaudin-type models associated to these solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_04440 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalized classical Yang-Baxter equation and regular decompositions Abedin, Raschid Maximov, Stepan Stolin, Alexander Rings and Algebras Mathematical Physics 17B38, 17B80 The focus of the paper is on constructing new solutions of the generalized classical Yang-Baxter equation (GCYBE) that are not skew-symmetric. Using regular decompositions of finite-dimensional simple Lie algebras, we construct Lie algebra decompositions of $\mathfrak{g}(\!(x)\!) \times \mathfrak{g}[x]/x^m \mathfrak{g}[x]$. The latter decompositions are in bijection with the solutions to the GCYBE. Under appropriate regularity conditions, we obtain a partial classification of such solutions. The paper is concluded with the presentations of the Gaudin-type models associated to these solutions. |
| title | Generalized classical Yang-Baxter equation and regular decompositions |
| topic | Rings and Algebras Mathematical Physics 17B38, 17B80 |
| url | https://arxiv.org/abs/2405.04440 |