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arXiv · 2503.10208

On the Jordan-Chevalley decomposition problem for operator fields in small dimensions and Tempesta-Tondo conjecture

Alexey V. Bolsinov·Andrey Yu. Konyaev·Vladimir S. Matveev
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Abstract

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 Fr\"olicher-Nijenhuis type.

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Alexey V. Bolsinov, Andrey Yu. Konyaev, Vladimir S. Matveev. 2025-03-13. On the Jordan-Chevalley decomposition problem for operator fields in small dimensions and Tempesta-Tondo conjecture. https://doi.org/10.1016/j.geomphys.2025.105656

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