• Corpus ID: 216253284

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

  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},
  • J. Bassi
  • Published 23 June 2018
  • Mathematics
  • arXiv: Operator Algebras
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… 
1 Citations

Tracial approximate divisibility and stable rank one

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



Purely infinite C*-algebras from boundary actions of discrete groups.

There are various examples of dynamical Systems giving rise to simple C*-algebras, in which hyperbolicity, or a weakened form thereof, precludes the existence of a trace. In these situations one

Dimension and Stable Rank in the K‐Theory of C*‐Algebras

In topological K-theory, which can be viewed as the algebraic side of the theory of vector bundles, some of the interesting properties which one investigates are, for example, the conditions under

Discrete Crossed product C*-algebras

Classification of C*-algebras has been an active area of research in mathematics for at least half a century. In this thesis, we consider classification results related to the class of crossed

Rokhlin Dimension for Flows

We introduce a notion of Rokhlin dimension for one parameter automorphism groups of $${C^*}$$C∗-algebras. This generalizes Kishimoto’s Rokhlin property for flows, and is analogous to the notion of

Lattice actions on the plane revisited

We study the action of a lattice Γ in the group G = SL(2, R) on the plane. We obtain a formula which simultaneously describes visits of an orbit Γu to either a fixed ball, or an expanding or


Let C(X) xT Z be the crossed product associated to a dynamical system (X , T). We give a necessary and sufficient condition for C(X) xT Z to have a dense set of invertible elements. When X is

Minimal dynamics and the classification of C*-algebras

It is proved that the crossed product C(X) ⋊α ℤ absorbs the Jiang-Su algebra tensorially and has finite nuclear dimension, so that crossed products arising from uniquely ergodic homeomorphisms are determined up to isomorphism by their graded ordered K-theory.


  • L. Robert
  • Mathematics
    Glasgow Mathematical Journal
  • 2015
Abstract It is shown that ${\mathcal{Z}}$-stable projectionless C*-algebras have the property that every element is a limit of products of two nilpotents. This is then used to classify the

Remarks on some simple $C^*$-algebras admitting a unique lower semicontinuous 2-quasitrace

  • J. Bassi
  • Mathematics
    Colloquium Mathematicum
  • 2021
Using different descriptions of the Cuntz semigroup and of the Pedersen ideal, it is shown that $\sigma$-unital simple $C^*$-algebras with almost unperforated Cuntz semigroup, a unique lower