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

arXiv eprints
 Pub Date:
 June 2018
 arXiv:
 arXiv:1806.09020
 Bibcode:
 2018arXiv180609020B
 Keywords:

 Mathematics  Operator Algebras;
 46L05;
 46L55
 EPrint:
 replaced with accepted version, to appear in Mathematica Scandinavica