On C^*-algebras associated to actions of discrete subgroups of SL(2,ℝ) on the punctured plane

2018/06/23 by Bassi, Jacopo
#46L05 #46L55 #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1806.09020

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,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,ℝ).

Related

• Group actions on Smale space C*-algebras
• Boundary maps and covariant representations
• Unitary representations of the Roe algebra of a discrete group and symmetries
• A Galois correspondence for reduced crossed products of unital simple\n C^*-algebras by discrete groups
• Rigidity theory for C^*-dynamical systems and the "Pedersen Rigidity Problem"