Mathematics – Operator Algebras
Scientific paper
2000-11-23
Mathematics
Operator Algebras
26 pages
Scientific paper
Let $\Gamma$ be a torsion free lattice in $G=\PGL(3,{{\mathbb F}})$ where ${{\mathbb F}}$ is a nonarchimedean local field. Then $\Gamma$ acts freely on the affine Bruhat-Tits building ${\mathcal B}$ of $G$ and there is an induced action on the boundary $\Omega$ of ${\mathcal B}$. The crossed product $C^*$-algebra ${\mathcal A}(\Gamma)=C(\Omega) \rtimes \Gamma$ depends only on $\Gamma$ and is classified by its K-theory. This article shows how to compute the K-theory of ${\mathcal A}(\Gamma)$ and of the larger class of rank two Cuntz-Krieger algebras.
Robertson Guyan
Steger Tim
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