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

  • Jacopo Bassi


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 $\operatorname{SL} (2,\mathbb{R} )$ 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 $\operatorname{SL} (2,\mathbb{R} )$.


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How to Cite
Bassi, J. (2020). On $C^*$-algebras associated to actions of discrete subgroups of $\operatorname{SL}(2,\mathbb{R})$ on the punctured plane. MATHEMATICA SCANDINAVICA, 126(3), 540-558. https://doi.org/10.7146/math.scand.a-120288