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

2025

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DOI 10.1016/j.geomphys.2025.105656
Data confidence 70 medium
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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 Frölicher-Nijenhuis type.