We are interested in global properties of systems of left-invariant differential operators on compact Lie groups: regularity properties, properties on the closedness of the range and finite dimensionality of their cohomology spaces, when acting on various function spaces e.g. smooth, analytic and Gevrey. Extending the methods of Greenfield and Wallach (1973) to systems, we obtain abstract characterizations for these properties and use them to derive some generalizations of results due to Greenfield (1972), Greenfield and Wallach (1972), as well as global versions of a result of Caetano and Cordaro (2011) for involutive structures.

中文翻译：

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紧李群上左不变微分系统的全局正则性和可解性

我们对紧李群上左不变微分算子系统的全局性质感兴趣：当作用于各种函数空间（例如平滑、解析和 Gevrey）时，正则性、范围的闭性和上同调空间的有限维数的性质。将 Greenfield 和 Wallach (1973) 的方法扩展到系统，我们获得这些属性的抽象特征，并使用它们来推导出 Greenfield (1972)、Greenfield 和 Wallach (1972) 以及全球版本的结果的一些概括。 Caetano 和 Cordaro (2011) 的对合结构的结果。