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

@article{Bassi2018OnA, title={On \$C^*\$-algebras associated to actions of discrete subgroups of \$SL(2,\mathbb\{R\})\$ on the punctured plane.}, author={Jacopo Bassi}, journal={arXiv: Operator Algebras}, year={2018} }

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 $SL(2,\mathbb{R})$ acting on the plane with the origin removed 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…

## One Citation

### Tracial approximate divisibility and stable rank one

- MathematicsJournal of the London Mathematical Society
- 2022

In this paper, we show that every separable simple tracially approximately divisible C∗algebra has strict comparison, and, it is either purely infinite or has stable rank one. As a consequence, we…

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