Boundary 𝐶*-algebras for acylindrical groups

Robertson, Guyan

doi:10.1090/S0002-9939-08-09453-7

Boundary $C^*$-algebras for acylindrical groups
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Proc. Amer. Math. Soc. 136 (2008), 3851-3860 Request permission

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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