paper

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

arXiv:2503.10208 · doi:10.1016/j.geomphys.2025.105656

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 , similar to a nilpotent Jordan block, to possess local coordinates in which takes a strictly upper triangular form. We prove the Tempesta-Tondo conjecture for higher order brackets of Frölicher-Nijenhuis type.

10 pages

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