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Boundary $ C^*$-algebras for acylindrical groups


Author: Guyan Robertson
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
Published electronically: June 3, 2008
MathSciNet review: 2425724
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Abstract | References | Similar Articles | Additional Information

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.


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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

DOI: https://doi.org/10.1090/S0002-9939-08-09453-7
Keywords: Acylindrical group, boundary, Cuntz-Krieger algebra
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
Article copyright: © Copyright 2008 American Mathematical Society

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