论文标题
广义的nijenhuis扭转和操作员领域的区块划分
Generalized Nijenhuis Torsions and block-diagonalization of operator fields
论文作者
论文摘要
由于Nijenhuis和Haantjes，广义Nijenhuis扭转理论扩展了经典概念，为研究正常形式的操作员领域提供了新的工具。我们提出了一个总体结果，以确保鉴于一个通勤的运营商领域的家庭，其广义的nijenhuis $ l $ l $消失了，就存在一个本地图表，可以同时将所有操作员同时进行封锁。我们还介绍了广义Haantjes代数的概念，该概念由具有消失高层扭转的操作员组成，作为一种新的代数结构自然概括了标准Haantjes代数。
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.
