On the Jordan–Chevalley decomposition problem for operator fields in small dimensions and Tempesta–Tondo conjecture
Bolsinov A.V. Konyaev A.Y. Matveev V.S.
December 2025Elsevier B.V.
Journal of Geometry and Physics
2025#218
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.
Haantjes torsion , Jordan-Chevalley decomposition , Nijenhuis torsion , Tensorial conditions for upper triangularisation of (1,1)-tensor fields
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School of Mathematics, Loughborough University, LE11 3TU, United Kingdom
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Faculty of Mechanics and Mathematics and Center for Fundamental and Applied Mathematics, Moscow State University, Moscow, 119992, Russian Federation
Institut für Mathematik, Friedrich Schiller Universität Jena, Jena, 07737, Germany
School of Mathematics
Institute of Mathematics and Mathematical Modeling
Faculty of Mechanics and Mathematics and Center for Fundamental and Applied Mathematics
Institut für Mathematik
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026