非自由变换群的收敛强度
Strength of convergence in non-free transformation groups
摘要：
设（G，X）是一个变换群，其中群$G$不一定在空间X上自由作用.我们调查G的行动可能失败的程度是适当的。稳定子群被用来定义新的概念，在轨道空间的收敛强度和措施积累沿轨道。利用伴随交叉积C^*-代数的表示论，证明了这些概念在一定条件下是等价的.
英文摘要：
Let (G, X) be a transformation group where the group $G$ does not necessarily act freely on the space X. We investigate the extent to which the action of G may fail to be proper. Stability subgroups are used to define new notions of strength of convergence in the orbit space and of measure accumulation along orbits. By using the representation theory of the associated crossed product C^*-algebra, we show that these notions are equivalent under certain conditions.
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