标题： 广义Nijenhuis挠率和算子场的块对角化 显示英文标题

标题： Generalized Nijenhuis Torsions and block-diagonalization of operator fields

摘要： 广义Nijenhuis挠率的理论扩展了由Nijenhuis和Haantjes提出的经典概念，为算子场的标准型研究提供了新的工具。 我们提出了一般性结果，确保对于一族交换的算子场，若其广义Nijenhuis挠率（$l$级别）为零，则存在一个局部坐标系，使得所有算子可以同时块对角化。 我们还引入了广义Haantjes代数的概念，它由高阶挠率为零的算子组成，作为一种新的代数结构，自然推广了标准的Haantjes代数。 显示英文摘要

摘要： The theory of generalized Nijenhuis torsions, which extends the classical notions due to Nijenhuis and Haantjes, offers new tools for the study of normal forms of operator fields. We propose a general result ensuring that, given a family of commuting operator fields whose generalized Nijenhuis torsion of level $l$ vanishes, there exists a local chart where all operators can be simultaneously block-diagonalized. We also introduce the notion of generalized Haantjes algebra, consisting of operators with a vanishing higher-level torsion, as a new algebraic structure naturally generalizing standard Haantjes algebras.