# Finite symmetry group actions on substitution tiling C*-algebras

@article{Starling2012FiniteSG, title={Finite symmetry group actions on substitution tiling C*-algebras}, author={Charles Starling}, journal={arXiv: Operator Algebras}, year={2012} }

For a finite symmetry group G of an aperiodic substitution tiling system (P,!), we show that the crossed product of the tiling C � -algebra A! by G has real rank zero, tracial rank one, a unique trace, and that order on its K-theory is determined by the trace. We also show that the action of G on A! satisfies the weak Rokhlin property, and that it also satisfies the tracial Rokhlin property provided that A! has tracial rank zero. In the course of proving the latter we show that A! is finitely…

## 6 Citations

### K-Theory of Crossed Products of Tiling C*-Algebras by Rotation Groups

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Let Ω be a tiling space and let G be the maximal group of rotations which fixes Ω. Then the cohomology of Ω and Ω/G are both invariants which give useful geometric information about the tilings in Ω.…

### K-Theory of Crossed Products of Tiling C*-Algebras by Rotation Groups

- MathematicsCommunications in Mathematical Physics
- 2014

Let Ω be a tiling space and let G be the maximal group of rotations which fixes Ω. Then the cohomology of Ω and Ω/G are both invariants which give useful geometric information about the tilings in Ω.…

### Classification of tiling $C^*$-algebras

- Mathematics
- 2019

We prove that Kellendonk's $C^*$-algebra of an aperiodic and repetitive tiling with finite local complexity is classifiable by the Elliott invariant. Our result follows from showing that Kellendonk's…

### Group actions on Smale space $\text{C}^{\ast }$-algebras

- MathematicsErgodic Theory and Dynamical Systems
- 2020

Group actions on a Smale space and the actions induced on the $\text{C}^{\ast }$-algebras associated to such a dynamical system are studied. We show that an effective action of a discrete group on a…

### Nuclear dimension and classification of C*-algebras associated to Smale spaces

- Mathematics
- 2016

We show that the homoclinic C*-algebras of mixing Smale spaces are classifiable by the Elliott invariant. To obtain this result, we prove that the stable, unstable, and homoclinic C*-algebras…

### C*-algebras of Boolean inverse monoids - traces and invariant means

- Mathematics
- 2016

To a Boolean inverse monoid $S$ we associate a universal C*-algebra $C_B^*(S)$ and show that it is equal to Exel's tight C*-algebra of $S$. We then show that any invariant mean on $S$ (in the sense…

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