多重连通流形上的叶状C ~*-代数
Foliation C*-algebras on multiply fibred manifolds
摘要：
受半单群指标理论的启发，我们研究了多重纤维化流形上的叶状C^*-代数之间的关系。设F_1，...，F_r是流形X的光滑叶理的集合.我们施加一个条件，确保他们产生的切向量场的李括号下的叶状F的局部同胚这些叶状。证明了沿每个F_j的纵向光滑算子的乘积属于沿F的光滑算子的C ~*-闭包。给出了紧李群上非交换调和分析的一个应用。
英文摘要：
Motivated by index theory for semisimple groups, we study the relationship between the foliation C^*-algebras on manifolds admitting multiple fibrations. Let F_1,...,F_r be a collection of smooth foliations of a manifold X. We impose a condition of local homegeneity on these foliations which ensures that they generate a foliation F under Lie bracket of tangential vector fields. We then show that the product of longitudinal smoothing operators along each F_j belongs to the C*-closure of the smoothing operators along F. An application to noncommutative harmonic analysis on compact Lie groups is presented.
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