关于与穿孔平面上$\operatorname｛SL｝（2，\mathbb｛R｝）$的离散子群的作用相关的$C^*$-代数

Pub Date : 2020-09-03 DOI:10.7146/math.scand.a-120288

J. Bassi

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引用次数: 0

摘要

确定了保证离散变换群C＊-代数稳定性的动力学条件。将结果应用于SL（2，R）的一些离散子群通过向量的矩阵乘法作用于删截平面上的情况。在共紧子群的情况下，从SL（2，R）的相应紧致齐次空间上与钟表圈流相关的C＊-代数的性质，推导出这种交积的进一步性质。

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On $C^*$-algebras associated to actions of discrete subgroups of $\operatorname{SL}(2,\mathbb{R})$ on the punctured plane

Dynamical conditions that guarantee stability for discrete transformation group C∗-algebras are determined. The results are applied to the case of some discrete subgroups of SL(2,R) acting on the punctured plane by means of matrix multiplication of vectors. In the case of cocompact subgroups, further properties of such crossed products are deduced from properties of the C∗-algebra associated to the horocycle flow on the corresponding compact homogeneous space of SL(2,R).

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