论文标题
一维单数叶的平滑代数
The smooth algebra of a one-dimensional singular foliation
论文作者
论文摘要
Androulidakis和Skandalis展示了如何将尸体类型，平滑的卷积代数和C* - 代数与任何单数叶叶相关联。在本说明中，我们考虑了矢量场给出的一维流形的奇异叶子，这些叶子在某个点上消失了。我们表明，尽管这些叶子的C*代数根据K的奇偶校而将两个同构类别分为两个同构类别，但平滑的代数是成对的非同构。这是通过分析平滑代数中的某些天然理想来完成的。出现了有关卷积的分解问题，并使用diximier-malliavin定理的上下文适当版本解决。
Androulidakis and Skandalis showed how to associate a holonomy groupoid, a smooth convolution algebra and a C*-algebra to any singular foliation. In this note, we consider the singular foliations of a one-dimensional manifold given by vector fields that vanish to order k at a point. We show that, whereas the C*-algebras of these foliations are divided into two isomorphism classes according to the parity of k, the smooth algebras are pairwise nonisomorphic. This is accomplished by analyzing certain natural ideals in the smooth algebras. Issues of factorization with respect to convolution arise and are resolved using a context-appropriate version of the Diximier-Malliavin theorem.
