## Boundary $C^*$-algebras for acylindrical groups

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## Abstract:

Let $\Delta$ be an infinite, locally finite tree with more than two ends. Let $\Gamma <\operatorname {Aut}(\Delta )$ be an acylindrical uniform lattice. Then the boundary algebra $\mathcal {A}_\Gamma = C(\partial \Delta )\rtimes \Gamma$ is a simple Cuntz-Krieger algebra whose K-theory is determined explicitly.## References

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## Additional Information

**Guyan Robertson**- Affiliation: School of Mathematics and Statistics, University of Newcastle, NE1 7RU, United Kingdom
- Email: a.g.robertson@newcastle.ac.uk
- Received by editor(s): June 29, 2007
- Received by editor(s) in revised form: October 5, 2007
- Published electronically: June 3, 2008
- Communicated by: Marius Junge
- © Copyright 2008 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**136**(2008), 3851-3860 - MSC (2000): Primary 20E08, 46L80
- DOI: https://doi.org/10.1090/S0002-9939-08-09453-7
- MathSciNet review: 2425724