高阶Haantjes括号与可积性
Higher Haantjes Brackets and Integrability
摘要：
我们提出了一个新的，无限类的括号推广Frölicher-Nijenhuis括号。这个类可以减少到一个家庭的广义Nijenhuis扭转最近推出。特别是，Haantjes括号，我们的建设的第一个例子，是相关的Haantjes模的运营商的特征。我们还将证明给定算子的高阶Nijenhuis挠为零是其广义本征分布可积的充分条件。这个结果（不需要任何关于算子谱性质的知识）推广了著名的Haantjes定理。相同的消失条件也保证了该算子可以在局部图中以块对角形式写出。
英文摘要：
We propose a new, infinite class of brackets generalizing the Frölicher--Nijenhuis bracket. This class can be reduced to a family of generalized Nijenhuis torsions recently introduced. In particular, the Haantjes bracket, the first example of our construction, is relevant in the characterization of Haantjes moduli of operators. We shall also prove that the vanishing of a higher-level Nijenhuis torsion of a given operator is a sufficient condition for the integrability of its generalized eigen-distributions. This result (which does not require any knowledge of the spectral properties of the operator) generalizes the celebrated Haantjes theorem. The same vanishing condition also guarantees that the operator can be written, in a local chart, in a block-diagonal form.
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