On the Jordan-Chevalley decomposition problem for operator fields in small dimensions and Tempesta-Tondo conjecture
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915913968648192 |
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| author | Bolsinov, Alexey V. Konyaev, Andrey Yu. Matveev, Vladimir S. |
| author_facet | Bolsinov, Alexey V. Konyaev, Andrey Yu. Matveev, Vladimir S. |
| contents | We explore the Jordan-Chevalley decomposition problem for an operator field in small dimensions. In dimensions three and four, we find tensorial conditions for an operator field $L$, similar to a nilpotent Jordan block, to possess local coordinates in which $L$ takes a strictly upper triangular form. We prove the Tempesta-Tondo conjecture for higher order brackets of Frölicher-Nijenhuis type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_10208 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Jordan-Chevalley decomposition problem for operator fields in small dimensions and Tempesta-Tondo conjecture Bolsinov, Alexey V. Konyaev, Andrey Yu. Matveev, Vladimir S. Differential Geometry Mathematical Physics Exactly Solvable and Integrable Systems 53A45, 58A30 We explore the Jordan-Chevalley decomposition problem for an operator field in small dimensions. In dimensions three and four, we find tensorial conditions for an operator field $L$, similar to a nilpotent Jordan block, to possess local coordinates in which $L$ takes a strictly upper triangular form. We prove the Tempesta-Tondo conjecture for higher order brackets of Frölicher-Nijenhuis type. |
| title | On the Jordan-Chevalley decomposition problem for operator fields in small dimensions and Tempesta-Tondo conjecture |
| topic | Differential Geometry Mathematical Physics Exactly Solvable and Integrable Systems 53A45, 58A30 |
| url | https://arxiv.org/abs/2503.10208 |